Danny,
For officer's names - especially where you have the initials and ranks - using the Air Force Lists would be of huge value to you. They are online free at the following website;
https://digital.nls.uk/british-milit...chive/97343434
You can download them too. For May 1940 names I would use the June 1940 list as the names are up to date to about mid-May. Even more useful when used in conjunction with the CWGC and London Gazette websites as Chris suggests.
For enlisted men, not so easy. The best source are the AIR 78 enlisted personnel name cards, free to download or view at TNA website. If you have a service number you can generally find the full name, but for one reason or another I would guess about 30% of the cards are unusable (initials only) or unreadable (blurred, too faint).
Squadron Appendices can be a huge source for names (initials and service numbers) if lucky. As I mentioned before 13 Squadron have as many as 5 Appendices for the 1939-1940 period.
regards,
Martin.