Ondro,
Thanks for your message. Interesting twist, I assume it is mostly your own suggestion rather than an official one by Payara (you are not the PMC rep there, are you?)
I don't know which exact options were condensed into a short-list, but I remember e.g. OpenEE or OpenJEE (should the acronym be allowed) were among more often suggested names.
I really don't see much difference between E4JEE and EE4J, if "JEE" was still acceptable then OpenJEE (similar to OpenJ9) or even OpenEE sound better as a brand for the "platform" as opposed to the EE4J TLP which most likely is going to stay.
None of the suggestions are without "JEE" or "JavaEE" so it s up to others to decide, if this is worth our time to discuss them. If "JEE" was OK then see above, it just spells more easily than any of the tongue-breakers and artificial contructions that nearly seem like the German party that once doomed the whole world...
Whether EE4J or any other EE includes "Eclipse" and "Enterprise" or "Enterprise" and something else (e.g. "Extension") that has not been finally confirmed either. It was put on some project pages, but it may not be written in stone, that one "E" could also stand for "Extension" or similar.