nope violent anger. the whole reason why the org members changed their names and added X's, was to be loyal to Xehanort, who had an X in his name, and to show as a sign of betrayal, towards Ansem.
If Axel was really alex, his org name would be Alex, not Axel, cuz there's no reason turning Alex into Axel if it already has an X in his name
ALL the org members annogrammed an X into their name, Axel wasn't Alex, otherwise they would have kept that name. And the rule applied for all members. Axel wasn't special, he would have had to annogram his name too. When roxas came to the org, his name was Sora, but Xemnas took him into the org because he could wield the keyblade, and annogrammed his name to become Roxas.