Gamertag taken even though no one else has it.

could be a tag set private or in use elsewhere on the system or even an old banned tag.

Hello, first it's a pleasure to be able to help you today.

My name is welcome to the community.

Hello Lt., since you deleted the account the Gamertag went along with it, the fact that you give up an account with the Gamertag does not release it for use immediately, it is suspended in the system, so you can have a Gamertag without suffixes should choose a Gamertag that has never been used before, or write the one you want in a different way putting numbers in place of letters for example.

https://social.xbox.com/changegamertag

Enter your own gamertag or select one of the suggestions:

If you're creating your own player information, type it and select Check availability.

If you receive a message that player information is already in use, you'll need to create others.

If you want to use one of the player information provided by Xbox but didn't like the suggestions, select Update to see other suggestions.

When you find available player information, select: Stay with it.

If the system says it's taken, then it's in use somewhere on Microsoft's services. The system doesn't see things like spaces as making a gamertag unique. So looking up "gamertag" may not show up even though it's in use as "gamer tag". The tag system is in
use on other Microsoft services as well, so even if it's not in use on an Xbox, it may be in use somewhere else.

Check this out, hope it helps.

Xbox Support

https://support.xbox.com/help/account-profile/profile/gamertag-update-faq

This is the new gamertag system - if you change it again you'll be given to choose both a "new" gamertag (with the numbers) and an "old" gamertag (without the numbers, and this is what will be displayed in just about everything that uses Xbox Live).