When registering in Valorant, you must enter your data - login (name, nickname) and password. Sometimes when users enter a login, it says "Username must be unique."
This means that this name is already taken by another player. In this case, you need to come up with another nickname. Perhaps add some numbers, additional letters at the end.
In order not to bother much with inventing a name on your own, you can use a free nickname generator. Go to service, select the first letter of the name, the number of characters and click on the "Generate" button. With each click, the service will generate a new nickname. You can use the one you like in its original form or change it for yourself.