Display names are a feature announced on the Roblox Developer Forum on February 7, 2021. The feature is similar to Twitter's display names, where on the user's profile, their selected display name would show up. Then, under it, a handle with their username. Display names can be changed once every 7 days. They cost no fees whatsoever and you can have the same display name as someone else or have someone else's username, with minor exceptions such as the usernames of famous Youtubers or Roblox moderators.
It was first released on February 18, 2021 for 1 hour in Germany, but then removed. It came back again on April 14th 2021. It was then shortly removed April 15th 2021 at 9:48 AM UTC time.
Display names to replace the player's username on the player list of a any game and username above the player. However, the chat will still display the username.
Display names are initial only seen on Roblox website in Germany, if not in Germany, you can't add a display name on the settings, but usage of a VPN could help you getting your display name and it will stay in-game even after VPN has been disabled but it will not show a display name on Roblox website (as of April 24th) 
It has been added back after constant removals on 12th May 2021
Users have criticized display names for how it is to impersonate developers or youtubers. However, Roblox has (at least attempted) disabled impersonating YouTubers/Mods by saying the display name is "inappropriate" when trying to type (e.g. TanqR, or ROBLOX). Results do not seem conclusive thus far due to people still having a display name like "ROBLOX" and other YouTubers such as "Puuung" or "mrflimflam".
For the first hour during the February 18th release, some players were able to put a swastika symbol on their profiles, but those accounts were quickly terminated. Some users were also able to put a foreign symbols in their usernames too, but their display names were reset.
Display names will appear on the leaderboard in-game. Players can click on a user's name in a leaderboard and it will show their display name and their username with @ sign. Also it will also appear in the menu. Developers can also enable display names to be visible in chat via going to Chat -> ClientChatModules -> ChatSettings: line 98, then copy the folder "ClientChatModules", to stop play testing and paste the folder into "Chat".