Xbox gamertag filters should be updated

If you're signed into the same Microsoft/Xbox account (registered to your gamertag) that purchased the games, they should appear on that page.

If you don't see anything, you'll probably need to adjust the filters (found under the words "Order History"). Adjust the filter to show "All" and the date range from "Past 3 months" to "All Available".

The most likely scenario is that that Gamertag is already in use but, as per the new Gamertag update you should be able to also have it with the advent of having a # and randomly assigned numbers in a smaller-ish font next to your name. If that's not the
case, I checked for you and did find someone with 'Crybaby' as their Gamertag, then it could actually be considered offensive due to it technically being an insult.

As for your friend, because the Gamertag uses a 'unique' spelling to bypass the profanity filter... the only way for it to technically be pulled for being offensive/profanity would be if someone put two and two together and reported it.

You should check this link out for more information about the 'new' Gametag update.

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

Xbox's gamertag filter can be a tad bit extreme when it comes to what is and isn't allowed. So what you may find to be okay, the filter will not.

Microsoft can't reasonably expect to program a filter that will catch all offensive gamertags. People are far too clever for that. If your gamertag was borderline then it's unfortunate, however it's likely that it wasn't, and you should have known better.

That means that the gamertag you're trying to use tripped one of the filters, meaning it can't be used at all (Their gamertag filters are a tad bit strict).