Every Roblox account has a username, and it can also have a display name. They may look similar on screen, but they do different jobs.
Your username identifies your exact account. A display name is the name people usually see above your avatar and can be shared by many players.
Your username is unique
Only one account can use a particular Roblox username at a time. It appears with an @ sign on profiles and is useful when somebody needs to search for the correct player.
Changing a username normally costs Robux. An old username may still be connected to the account so that changing it cannot be used to completely hide who owned it.
Display names are more flexible
Display names do not need to be unique. You might join a server and see several players using the same name, which is why moderators and support teams ask for the username or user ID instead.
Roblox lets users change a display name without paying, but limits how often it can be changed. Both names still pass through Roblox moderation.
Which one should you share?
Use your username when a friend is trying to find your exact profile or when you report a player. Check the @username rather than trusting the large display name alone.
Neither name should include private information such as your real surname, school, phone number or address. A fun nickname is enough.