Can I simply convert Unfiled Groups into My Groups with the same name?

I have 30 unfiled groups that were shared with me. Is there a way to turn them into My Groups of the same name without creating 30 new groups and then moving the references in each Unfiled Group into mine?

Yes you should be able to move all groups from the Unfiled Groups folder to an existing group set in EndNote. If an appropriate group set does not currently exist, then you should create one. EndNote removes the Unfiled Groups folder from the Groups panel when you move all unfiled groups to a group set.