Every Colonist account comes with one free username change. Once you've used it, any future rename costs 1,300 Colonist Coins, which you can purchase in the store.
If the free rename option appears unavailable, check the following:
You already used your free rename. Each account only gets one. If you've changed your username before, the free option is no longer available. You'll need to spend 1,300 Colonist Coins for any further changes.
You're logged into the wrong account. Make sure you're signed into the correct account - especially if you have multiple accounts or previously played as a guest. Your free rename is tied to a specific account.
Your username was changed by a moderator. If your username changed and you didn't do it yourself, it was most likely renamed by a moderator for violating our naming policy. In this case, the original name was replaced with a auto-generated one. This doesn't count as your free rename, so you should still be able to change it once on your own.