This community gave me a default name that I want to change. I tried "edit profile" and there wasn't an option. What do I do?

Not sure you can edit your Apple Support Community Name. I don’t believe they use an Apple ID due to that typically being an email address. When you first establish your Apple Support Community relationship you should have had an opportunity to establish your own ID as long as your choice was available.

I just noticed a post under “Communities” in the view other: that was labeled something like using this community support forum that asked if their name could be changed and someone replied that they had passed the request on to the correct person. You might want to repost your request under that topic and see if someone does the same for you. It was called: “Using This Community “

Only the hosts of this site can change usernames. I have notified them of your request. Expect an email from them.