To change you name in Valorant you need to go to its owner website, means the Riot games website which developed the games, yes its little weird but they made it quiet simple from there that we will discuss in this post.
To change your name in valorant follow these step
first go to Riot Account webpage and login with your credentials, you will receive a login code on your registered email to continue access to your account on next page.
after that, you can see your account info. from here you can edit or update whatever you want for your account.
so edit the things that you want and click save to confirm.
that's it now the changes will be saved and you will instantly see the updated info like the name of your valorant account, on valorant game, if the game was already open then you will need to restart the game in order to see the updated informations.