I also don't put my name's accent in most computer systems in the US (é). I have it on Linkedin though, and it trips a surprising amount of automated recruiting emails.
as a french... euh quoi ?
I kept expecting it to cause her problems, but it doesn't seem to have. Of course, dealing with the government means she has to use her first name sometimes, but that's it.
Anyone who knows me calls me by a nickname that isn't documented anywhere, for reasons too long and too boring to go into. It's worked out for me, as generally speaking, if someone calls looking for someone with my legal given name, it isn't someone whom I want to talk to!
I changed my last name to my very different middle name, leaving me with no middle name (and thus no initial, alas!). People who have not changed their names overestimate how much anyone cares. For instance, some credit card companies allow you to change your name online. Then they help to perpetuate the change by reporting it to the credit agencies.