I have an account with godaddy and I want to register a domain name for a friend. Can I do that or will it come up with my details as the owner, administrative person and billing details? Or will it all just show his stuff?

Whoever you input as the registrant, either your name or that of
your friend, is the legal owner of the domain name. But why can't
your friend register it for himself/herself?

Easiest way to do this is register it yourself and transfer it to his account.