Whose name appears on the sign-off of a disengagement letter?

The client's own, in the default template, since they're the one signing.

The default Disengagement letter template ends with an Acceptance section for the client, filled in with the [PrimaryContact] and [Name] placeholders (the client's primary contact and the client's name). It has no practice sign-off.

If you want one, you can add it to the template in Settings > Document content > Document templates, using insert placeholder to add a staff placeholder such as [Current User] or [Manager].

You can still choose which mailbox sends it at the point of sending, as long as that mailbox is linked to a staff member.