You need to close the game client and log in to the Riot website to change your name in Valorant. After signing in, go to the Riot ID tab and press the pen icon next to your Valorant show name. This gives you the choice to pick a new name and a special hashtag. Enter a new name to validate usability. Save it, if available. Once the modifications are saved, start Valorant on your system and you should do well.