To check if a name is available without a suffix, you must adhere to these specific formatting rules: Xbox gamertag FAQ
Several factors contribute to the unavailability of gamertags. The most obvious is the sheer number of Xbox users. With millions of active accounts, the demand for unique identifiers has skyrocketed. Another factor is the practice of gamertag hoarding, where players claim and then do not use certain tags, simply to prevent others from using them. Additionally, Microsoft's policies on gamertag changes have evolved over time, making it more difficult for players to change their tags without significant effort.
If someone changes their tag, the old one is held for before it can be claimed again.