It's quite possible there were details mis-typed; depending on source C4623 had 5 different engines fitted, WD 18592, 39398, 39399, 30399, 32612! As you say not likely for an aircraft to have 2 names ---a photo of the donor's inscription on it's first aircraft was usually sent to them and a record kept but increasing numbers of donor's (I believe about 600) led to problems.
C4623 was certainly received by 1AFC on 19 March 18 at Medjel, they had 17 serviceable and 2 unserviceable Bristols then.
This may be useful in future, the Sqn's War Diary Jan.-Nov.1918, lots of good stuff for research including serials.
Regards
Nick
https://www.awm.gov.au/collection/C1338817