I’ve put a lot of thought into tackling this same issue myself. The best thing I’ve come up with is this:
John Matthew Smith
1. Change surname, nobody really thinks twice about surname changes.
John Matthew Jones.
Or, if that’s not enough.
2. I’m going for flipping forenames AND changing the surname.
Matthew John Jones.
Then you can say you “used to go by your middle name”. You can still be known by John to some people. Any certificates ‘made a mistake' with the order of the name.
This isn’t a 100% water-tight method, but as I say, it’s the best I can think of. I'm all ears for any other ideas as I'm struggling too.
Fighting or Accepting - its difficult to know which is right and when.