The mechanics
Account Settings → Account Info → edit username: the change costs 100 Robux and takes effect immediately. Your friends list, items, groups and game stats all stay attached — only the handle changes. Your old username is reserved against reuse for a period, and the display name (a separate free-ish feature) can differ from the username.
Naming rules
Usernames are 3–20 characters, letters/numbers/single underscore, no spaces or symbols. The filter blocks personal information and flagged words. Display names (the friend-facing name) are more flexible and change free, so many players keep a stable username and iterate the display name instead — the smart move for creators whose brand lives in their username.
Creator brand advice
If you run games under a group, the group name is your brand and the personal username matters less. If your username IS your brand (game credits, socials), pick one you can say out loud on a stream and never need to re-buy — every rename is 100 Robux you did not spend on ads.