No, it's not true of those who preceded us. It seems it's a way to handle having new shinki appear with no bonds. However, naming a shinki is the normal, accepted way of acquiring one.

To do so with a shinki who belongs to another god makes that shinki a stray. They are looked down upon, and most gods with strays use them for dirty and dangerous work, to avoid polluting their original shinki.

If you want to remove a name you'll have to revoke it actively.

[He moves at last to pull Roxas's cell phone out of his pocket and toss it Roxas's way with a gentle underhand. He's not getting too close: again, it's just easier to keep himself under control if he doesn't. His voice has stayed even and chilly throughout, and that's as calm as he's going to be.]

Don't do things if you don't know the implications, Roxas.