To my knowledge, the travel arranger "Self-assign" permission isn't able to be limited in that way. It's a permission branch from the admin tree; however, if instead of "self-assign" permission, the travel arranger simply had ability to book for "guest," then they'd be booking without the users profile. If booking flight, they'd need to get the DOB some other way since "guest bookings" are made without access to travelers' profile. I'm not sure there's a middle ground to allow a user to access only a select portion of another user's travel profile.
