I am wondering why the url is ham.SE instead of amateurradio.SE or ar.SE. Is there a reason for this?
I wasn't here for that decision, but I can provide some informed speculation:
Short domain names are nice, and most
*.stackexchange.com names are kept as short as they can be while being reasonably unambiguous.
“Ham radio” or even just “ham” is a very popular name for amateur radio. It's unambiguous, because there's unlikely to be a SE site about one kind of meat.
“amateurradio.stackexchange.com” would be atypically long, and “ar.stackexchange.com” would be more likely to conflict with some other subject and not be as immediately recognizable to the people who would be interested.
This site is named ham.stackexchange.com because we wanted a site name that indicated the site is for Amateur Radio. The SE staff originally was going to name it Radio, but there were a number of us who convinced them to try something else, that was specific to Amateur Radio. Amateur, AmateurRAdio, etc were all too long. Ham or HamRadio were my preferred options, and in the end they chose Ham.SE.
See https://area51.meta.stackexchange.com/questions/12085/url-for-this-site for the original topic that changed the name to Ham.SE from what had been previously considered.