Probably not. In "Engame", the Voyager finale, Admiral Janeway has her shuttle and it is hers but probably only in the sense that she is allowed to use it as and when she wants, but if she were to die or to be fired from the post, it is possible she would lose the shuttle and it would be given to whoever is given the post after her. This is because the Federation is akin to a communistic society, and and Federation ships belong to the Federation as opposed to the "owner". However, it is also entirely possible that members of Starfleet have their own personal shuttles for personal business, in the same way that Nelix still has his personal ship aboard Voyager, but goes on the Federation shuttles on away missions. If Starfleet personnel do have their own ships, they would be bought privately.