How Do I Purchase/Change My Gamertag On The Xbox Website?

There is no way to change your Gamertag without a system as stated in the following article:

account.xbox.com/.../changegamertag

"How to change your Xbox gamertag"

Here's a link to a website that literally checks if a GamerTag is even available on Xbox in the first place!

"How to tell if a xbox gamertag is available

This website will tell you how
https://support.xbox.com/en-GB/my-account/manage-gamertag-and-profile/change-xbox-live-gamertag

Please note, the website I gave you only takes you to the old gamertag system, if you want to use the new gamertag system (free for 1st use), you can do so here

https://social.xbox.com/en-gb/changegamertag

Hello Rye,

Thanks for keeping us updated. Where exactly are you trying change your sons gamertag? There are a couple platforms you could do this on. You can change gamertags on the console or on the website. I recommend trying the alternative method to the one you
have been attempting to see if the issue persists.

How to change your Xbox gamertag

If you have been trying from the website, then you can also try using a different browser or a different device entirely.

Hope this helps!

that would be a randomized name

so do a namechange

if your gamertag on xbox live is my emotions then recover the account

if you mean your profile name on your console then you will have to promote3 that account to live account

if it says it is taken you will have to create a nother name