A. Shiphrah and Puah are names of clans, like tribes that were later called by those names after the skill of their eponymous ancestors in the work of childbirth. Like the Letushim in the book of Genesis or the Sukkites in Chronicles… Look into it.
B. It is an illustration of the righteousness of these two, who merited “houses.” But there were thousands of other midwives; only these became famous.
C. Onomatopoetic names (Rashi), as a designation for midwives.
D. In their dealings with Pharaoh, these were women holding a senior position, something like ministers over the midwives. (Like Joseph’s brothers, whom Pharaoh asked to be officers over his livestock.)
And I could go on.

See here for several interpretations:
https://mg.alhatorah.org/Full/Shemot/1.15#e0n6
I copied a bit of what I saw:

Ibn Ezra, first interpretation: “To the midwives” — they were officials over all the midwives.

Second interpretation: “And he said” — there is no doubt that there were far more than five hundred midwives; these two were officials over them, to give tax to the king from the wages, as I have seen even today in many places. And that they were mother and daughter is a received tradition (Babylonian Talmud, Sotah 11a), and it is plausible.

Shadal: And I say that Pharaoh did not want to speak with all the midwives at one time, for if all of them killed the Israelite babies at the same time, the matter would be noticeable and become public. But if only two of them killed them, and not the others, they could say it was just chance. His intention was to command all the midwives this way one after another, in rotation, so that the matter would not become known.

Nachmanides (can perhaps be combined with Shadal?): “…And it appears that this lasted only a few days, for when Aaron was born there was no decree, and when Moses was born it seems to have been canceled. Perhaps Pharaoh’s daughter, in her compassion for him, told her father not to do this; or when it became known that this had happened by order of the king, he canceled it; or it was due to the astrologers, as our rabbis said (Exodus Rabbah 1:29), for all of this was scheming against them so that the violence would not become known…”

Rabbi David Zvi Hoffmann: “The name of one…” — apparently these two were the heads of the community of midwives, who were required to convey the king’s words to their colleagues in the profession; compare Ibn Ezra and others.

Chizkuni: “Shiphrah, Puah” — some explain: there were many midwives in Egypt, for these two alone would not have been enough for six hundred thousand. Rather, these two were officials over all of them.

Rabbi Joseph ibn Kaspi: “And the king of Egypt said to the midwives” — this was another decree, and these midwives were superior over all the others, for it is possible there were more than they.

Abarbanel: “…As for the midwives, it is impossible to say that there were only two, for how could two women suffice for so numerous and mighty a people as the children of Israel? And one cannot say that they were only two who were officers over all the midwives, as the commentators say, because Scripture should then have called them officers of the midwives, as it says chief cupbearer, chief baker, and chief butcher. Also, what good would Pharaoh’s plan have done by speaking to the officers if he did not command their attendants as well? And moreover, he did not command them to pass this on to the midwives under them. Rather, the matter is as follows: it was the practice in Egypt that two midwives would come to attend each woman giving birth. One dealt with bringing out the baby and caring for it, and therefore was called Shiphrah, because she made the baby fair and presentable. The second dealt with supporting the woman in labor and helping her with words, sounds, and prayers, and therefore was called Puah, from the expression ‘I cry out like a woman in labor.’ And it says that Pharaoh spoke to the Hebrew midwives — meaning to all of them, for he did not speak to just two midwives. Rather, he spoke and gave this command to all the many midwives, and they were all divided into these two professions. This is the meaning of ‘the name of one was Shiphrah and the name of the second was Puah.’ And they were not Hebrew women, for how could he trust Hebrew women to kill their own children? Rather, they were Egyptian women who acted as midwives for the Hebrew women — that is, helped them give birth, as it says, ‘when you act as midwives for the Hebrew women.’ Now these midwives, though they were Egyptians, feared God and did not do what the king of Egypt had commanded them, so he rebuked them for it, saying, ‘Why have you done this thing and kept the children alive?’ This verse is not merely a repetition in different words. ‘Why have you done this thing’ means that they did not kill the children as he commanded them. Therefore he spoke in a somewhat indirect way: ‘Why have you done this thing?’ And he added, ‘and kept the children alive’ — meaning that not only did they not kill them, but they also actively worked for their survival, rescuing and feeding them as they emerged from the womb, so that they actually gave life to the children, the opposite of what he had commanded. And the midwives answered him in self-defense, saying, ‘For the Hebrew women are not like the Egyptian women, for they are lively’ — meaning that in caring for and tending the children, the Hebrew women are not like the Egyptian women, who do not know what should be done for their children and rely on the midwife. The Hebrew women are not so, for ‘they are lively’ is like the phrase ‘a living man of great deeds’ — meaning energetic women who actively care for their children and keep them alive…”

Sforno: “To the Hebrew midwives” — to those who were in the city of Egypt, for among so numerous a people there were certainly not only two midwives. But after the Egyptian midwives betrayed the king, even after the king had spoken to them personally, he no longer thought to trust the midwives in the other places.

Rabbi Moshe Alsheikh: “And God dealt well…” — now, the fact that ‘the people multiplied and became very mighty’ is a benefit to the people, so how can it say ‘and God dealt well with the midwives’? Rather, the midwives were caught between a rock and a hard place, saying: Woe to us because of Pharaoh, woe to us because of Israel. Because Pharaoh would not believe that we could not manage to attend the Hebrew women and that they gave birth without a midwife. And woe to us because of Israel, for if any of the children were born weak, or with a broken leg or arm, or anything similar, who could stop the people from saying: this is only because the midwife, seeking to do Pharaoh’s will, tried to kill him and could not, but only managed to weaken him or break one of his limbs, because God did not let her kill him — and she would be suspected of bloodshed. Therefore God did the midwives two kindnesses. One, that ‘the people multiplied’ greatly, to such an extent that Pharaoh would believe that two midwives could not possibly suffice for them, not even for one in a thousand of the births. And regarding the people’s suspicions, ‘and they became very mighty’ — all the babies were born robust, healthy, and strong, so there was no room at all to suspect them.

Or HaChaim: “…‘To the Hebrew midwives’ etc. — we need to know what He said to them in this statement. Perhaps the statement was that he called out and said: ‘the Hebrew women, one of whose names was…’ because many came before him and he did not recognize which ones were the midwives, so he called them by name in order to direct the speech to them, since they were the leading ones among all the midwives and he wanted to place the matter upon them, for such is the way of authority. Another possibility is that by this calling he made them great and officers over all the midwives, and that is why he specified their names. Therefore it says a second time, ‘And he said, when you deliver the Hebrew women…’ meaning that the command was not only to these two but to all the midwives, except that these would be officers over them…”

Malbim: “And the king of Egypt said” — according to the plain meaning, he said this to the Egyptian women who served as midwives for the Hebrew women. There were two kinds of midwives: one dealt with the woman sitting on the birthstool, to bring out the baby, and the second dealt with the newborn, to cut its umbilical cord and care for its needs. One was called Shiphrah and the second Puah. This does not mean there were only two midwives, for they were a numerous people. Rather, it means two kinds of midwives. Or, as Ibn Ezra says, the two were officers over all of them; and this is also how Don Isaac Abarbanel explains it…

Netziv: “The name of one was Shiphrah” — according to the plain meaning, if these are their names, then obviously they alone were not serving as midwives for all Israel, who lived in many cities. Rather, they were the chief midwives, and by Pharaoh’s command they would instruct all the midwives under them. The midrashic interpretation is known and explained in Rashi. That interpretation comes from the fact that ‘and he said’ is written twice. The first statement was what is known about the work of the midwives — one beautified the baby and the second soothed it — and now ‘and he said [again], when you deliver…’ And even according to that interpretation, he warned the chief midwives, and they would warn the midwives under them. See verse 18.

Very nice. Thanks for the effort.