And unique usernames don't solve that problem either. If I know a guy named "Mohammad Mohammad" and I want to find him on LinkedIn, I already don't know his unique username should he have one.

If I know him in person and ask for his LinkedIn, he can just send me a link to his profile. If Mohammad is advertising his LinkedIn presence, again, he can provide a link to his profile. Adding in unique usernames doesn't help much in this case.