As mentioned, allowing users to easily change usernames (let's call it "display name" to disambiguate) makes it easier for users to dodge the consequences of harrassharassing or scamscamming other users. If your site has a social aspect, maybe consider whether bans, blocks, reports, chat histories and the like between users, etc will carry through a username switch (ie will a user be aware that they are talking to the same account, even though the name has changed?).
Another point to consider is anonymity or privacy concerns. It's fairly frequent that someone makes an account with their real name and then posts something they regret and wishesfor whatever reason regrets attaching their real nameidentity to no longer be publicly visibleit. Sometimes this is because they were caught bullying or the like, but is often for legitimate reasons as well like over-sharing personal details of their life, or they become the victim of bullying. This recent question comes to mind as ana different example:
I accidentally entered password for a website as a username for another website
In this case, submitting a service ticket to be reviewed by a human sounds likeor allowing a limited number of account name changes sound like reasonable approachapproaches.