Answer 1

I've searched the net and yes you can but not your starter
When a Pokemon evolves at luminous spring it asks you wether you want to change its name otherwise it changes automatically into its new evolution name
As I said this does not apply to your starter but may for your partner
If you want to change team name it's on the menu at the start

Comments

I knew that, but I have a Nosepass whose name I'd like to change and it's already named Nosey. It didn't let me change it when it evolved into Probopass. What do I do?