[name].app or [name]api.com

I am trying to make an API for a game I like and I need to choose a domain to host it on.
Should I just choose

[name].app

[name].app

[name].app

[name].app or

[name]api.com

[name]api.com

[name]api.com

[name]api.com. I'm open to other suggestions of course let me now.

If using

[name].app

[name].app

[name].app

[name].app the endpoints would be

api.[name].app

api.[name].app

api.[name].app

api.[name].app

docs.[name].app

docs.[name].app

docs.[name].app

docs.[name].app

If using

[name]api.com

[name]api.com

[name]api.com

[name]api.com the endpoints would be

[name]api.com/api

[name]api.com/api

[name]api.com/api

[name]api.com/api or

api.[name]api.com

api.[name]api.com

api.[name]api.com

api.[name]api.com

[name]api.com/docs

[name]api.com/docs

[name]api.com/docs

[name]api.com/docs or

docs.[name]api.com

docs.[name]api.com

docs.[name]api.com

docs.[name]api.com