Most of the combat aviators I've known were pretty fond of their machines, as long as the birds brought 'em back. No doubt you could conduct a Psych 101 study on the subject, but airplanes almost as much as ships lend themselves to personal attachment. The difference is, of course (especially in WW I) that hardly anybody flew just one airplane--Barker being the notable exception. One sentiment specifically expressed was
Hamilton Coolidge of the 94th Aero who wrote his family, "My faithful old SPAD has to be replaced and I shall receive a horrid new one."
As for names, the practice was widespread.
Ray Brooks' famous "Smith IV" is perhaps the best known example in the US. (Michael's right about the often lengthy official names of some British presentation machines!)
Related subject: nose art, which rose to grand heights (no pun intended) in WW II now is almost gone. A few years ago a B-1 pilot told me that the wing nose art committee consisted of the wing commander, his wife, and the base chaplain. You may imagine the constraints on a fine old tradition...