- We can assume that the user (full) name is usable as the billing profile name (default on the create form), but can't assume the opposite
- Therefore we can't allow finding a user by billing profile in Commerce core, by default. That stays in contrib
- However, there should be a solution that: 1) adds a name field to the user 2) alters the user display name 3) alters the autocomplete (search by name, username, email)
The https://www.drupal.org/project/name module is close and could be documented on implementing this.