I grew up calling it "tunafish," but most people nowadays just seem to say "tuna," so I do sometimes, too. Although I haven't gone so far as to start calling soda/coke "pop." So I don't think it's all Americans who call it tunafish, just some? I don't know if it's regional, going out of fashion, or what.
I like mayo, sweet relish, and sometimes celery and/or lettuce in my tunafish. Never egg. I love hardboiled eggs and hardboiled egg sandwiches, I just can't imagine mixing that with tunafish. Oh, and I don't like mayonnaise in other stuff, or on my bread when I make sandwiches, but I do like it mixed with tunafish. I'm also not a big fan of when you get a tunafish sandwich somewhere and they use a ton of mayo and it's all drippy. Ick.