BuddyPress.org

For stuff like this, the fastest and easiest thing to do is just look at the template files you’ll be modifying for your child theme, the stuff in bp-themes/bp-default to see how it’s done. Have a look at /bp-themes/bp-default/members/index.php for example.

You probably want bp_get_loggedin_user_fullname(). See here, too: https://codex.buddypress.org/developer-discussions/buddypress-template-tags/