Ok, first of all, Aejon sound's awful. Stop trying to link the name Ned gave him to Lyanna's name.
Secondly, his name cannot also be Aegon since Rhaegar already named one of his children Aegon. I doubt Lyanna knows that, but I also doubt GRRM would write their names the same.
The only thing that really makes sense is Aemon, because of the various quotes people have posted and the fact that he met Maester Aemon. To me, it just seems very poetic.
If that isn't his name then it's probably something completely different like Daeron or Daemon or something.