Another interpretation: [Shiphrah is so called] because Israel was fruitful and multiplied [paru ve-ravu] in her days. Puah, this is Miriam; and why was her name called Puah? Because she would coo [po'ah] to the newborn.
Puah Is Miriam Who Cooed to the Newborn
Yalkut Shimoni on Torah 164:4
דָּבָר אַחֵר, שֶׁפָּרוּ וְרָבוּ יִשְׂרָאֵל בְּיָמֶיהָ. פּוּעָה זוֹ מִרְיָם, וְלָמָּה נִקְרָא שְׁמָהּ פּוּעָה שֶׁפּוֹעָה לַוָּלָד,