I split your post as the other thread was about user name changes not changing the name of the Sim.
You should be able to change the name by going to CAS but you will probably need to wait until they're toddlers. You can't change the name of babies (not sure on the current status of this)
If you really want control of the baby to further your storyline you can edit all aspects using a cheat code after they age up to a toddler.
First hit Control and c at the same time. A white rectangle will appear across the top of the screen. Click inside and type testingcheats on and hit enter. Then type cas.fulleditmode and enter. Now shift click on the toddler and select edit in create a sim. Now you can fully edit the entire family as if you were creating them for the first time. Gender body/face features.... everything.
