Is it obligatory to name the newborn "Muhammad" according to the vow, or is it permissible to name him "Yusuf" in response to the mother's request?

No other fast, even if it is a Sunnah fast, can substitute for a missed compensatory fast, based on the Hadith of Aisha (may Allah be pleased with her): "I would have a fast due from Ramadan, and I would not be able to make it up until Sha'ban."