Can you change gamertag if done new one by accident

Sorry, but no. There's no way to get another free change.

Hey Anthony,

Upon creation of an Xbox account, you are assigned a randomly generated
Gamertag which you are allowed to change once for free. Afterwards, any Gamertag change will come with a fee in this case the 10 Euros. It could be that the one time change was done accidently, resulting in the fee showing upon on your end.

Hi,

You can change the gamertag by simply paying for a gamertag change ($10). This can be done by following the directions
here.

As far as changing the gender of your avatar you'll need to delete your current one and make a new one. The avatar itself isn't connected directly to the gamertag. You can simply change the avatar and make a new one keeping the same gamertag. That can be done
in the avatar editor on the Xbox 360 console or at this link here.

That is normal

As that is your classic gamertag.and the new one is your current gamertag

You can change the classic under customize.my gamertag. Under your account settings

This is because.not.all games .support the new gamertag system

If you had done it on a xbox one or higher console you would've been given an option to customize your classic upon creation of the new one

For the sake of account security, I changed the account login and after that I inadvertently changed the gamertag to another one and now when I start the games I get an error.

What do you mean you "inadvertently changed the Gamertag"? Did you by accident create a new Microsoft Account instead of changing the sign in alias of your existing account? Because changing the Gamertag can only be done on a specific website or on the console
and will cost you the equivalent of about 10 US$.

As for account security: The only way to make your account secure is by enabling Two Step Verification on

https://account.live.com/Proofs/Manage.

Changing a login name is simply "Security through obscurity", and is not a method to make something secure.