Thankfully, for steam your username is not displayed to any other person. You have a profile ID (globally unique, alphanumeric, you can change as many times as you want), and a profile name (not unique)
Unfortunately for Steam, your login username is still displayed in some places like the top right of the Steam app and any computers you choose to share your library on.
It's also likely that they used the login username as a primary key, which means it's unlikely to be able to be changed anytime soon.
you can't change your profile id though. That's what's called a "steam id". You can change the URL (steam custom url) however. But accessing your profile with the steam id will still work.
Depends what's associated with the account, no?
If it's something like Steam, your username might be tied to hundreds of dollars of purchases.
If it's Slashdot, you'll lose your sweet low user ID.
If it's StackOverflow, you'll lose your various reputation scores.