Riot Games, the developer of Valorant, allows players to change their in-game display name once every 30 days. This guide will detail the steps needed to change your Valorant name.
1) Log in to your Riot account
Go to www.account.riotgames.com and use your Riot Games username and password to log into your account.

2) Change your Riot ID
Once logged into your Riot Games account, find the Riot ID area under Account Management.

Type in your new Riot ID using 16 characters or less. The Riot ID you choose must comply with Riot Game’s guidelines for profanity.
You can also choose a new Tagline for Valorant in the Riot ID area. Taglines are unique identifiers displayed as a hashtag followed by 3-5 characters, similar to a clan tag. Taglines allow multiple users to share the same Riot ID display name and can be used to invite friends in-game.
3) Confirm your new Riot ID
When satisfied with the new Riot ID and/or Tagline you’ve chosen for Valorant, press Save Changes to confirm.
The new Riot ID and Tagline you choose will be your display name for all Riot games, including Valorant.
Note that you can only change your Valorant name once every 30 days, so choose your new moniker wisely.