Upvote:1
Short version is that you would have been fine with Phil on the ticket, although your full name would have been needed to be provided during check-in in order to pass to the various government agencies both all countries you are going from/through/to (generally referred to as "APIS" data, although technically the name varies between countries).
This thread on FlyerTalk contains the text taken directly from the United Airlines staff systems on this topic :
NAME CHANGE GUIDELINES: **NOTE: IT IS NOT NECESSARY TO CHANGE A NAME ON A TICKET THAT INVOLVES A SIMPLE ERROR ON THE NAME, SUCH AS NICKNAME, MISSPELLING, OBVIOUS TYPO, NAME REVERSAL CHANGES WITH DOCUMENTATION OF MARRIAGE/DIVORCE. FOR INTERNATIONAL TRAVEL, UA MUST ENSURE ACCURATE APIS DATA IS COLLECTED AND IT MATCHES THE PASSPORT. FOR EXAMPLE, THE NAME ON THE TICKET CAN BE JON SMITH WHILE THE PASSPORT REFLECTS JONATHAN SMITH. APIS DATA MUST REFLECT JONATHAN SMITH - EXACTLY AS SHOWN IN THE PASSPORT, BUT NAME CHANGE TO THE TICKET IS UNNECESSARY.
Your case is obviously exactly the same as the "Jon/Jonathan" example given, so would have been completely acceptable and there would have been no need to update the ticket, just to provide the full name during check-in.
If you did really want to make sure the name was correct, there's 2 options. One is to wait for the name change process that you've started to complete and then rebook the ticket. I went through that very process with United a few weeks ago (to add a middle name to my account, but basically the same as you - a minor change backed by documentation). My request was submitted on a Thursday, and completed late the following Monday. I don't know if that's the usual response time or not (I do hold high status with United so may have been given priority, but I doubt it for a request like that).
The second option is that United allows you to spend your miles to make a booking for "someone else". You could use that process and instead of making a booking for yourself, you could make a booking for a different person with your exact same name - except obviously with the first name "Philip". The only downside to this is that your frequently flyer number would not be attached to the booking (because the ticket isn't for "you"), and you likely couldn't add it due to the name mis-match - but for an award flights that's likely not a problem, and even if it is you'll be able to add the Mileage Plus number once your name change has been processed.