changing login name on my Apple TV

In addition to the above, here’s some thoughts from a slightly different perspective.

What is your model Apple TV? Identify your Apple TV model - Apple Support

What is its version system software?

Apple TV (4th generation or later) has some account options that prior models do not have.

• To change the email of your Apple ID account, while keeping that same account with all its linked services, see: Change your Apple ID - Apple Support
• To change the screen name on Apple TV (4th generation or later): Settings﹥Users and Accounts﹥[You]﹥Edit User Name for Apple TV﹥.

Hi LDQuestions, Apple Support provides a good document for your question.

Share Apple TV with multiple users - Apple Support

I assume from your question you want to switch accounts but not entirely change the AppleID default user (the AppleID used to setup the AppleTV). This will be in Settings>Users and Accounts. You'll see you, the "Default User", as well as "Add New User". You can add a second AppleID login and the document will provide how to switch to it when needed. Note, I strongly suggest review the document as adding a second AppleID does not change the AppleID, for example, for iCloud.