You can change your gamertag on an Xbox One just by editing your user profile. It's free to change it once, and $9.99 each time afterwards.
You can get Xbox Live by signing up for a Microsoft account through the Xbox website or your Xbox One console.
If you’re looking for your perfect Xbox gamer tag, you’ll have a few more options to choose from soon. Microsoft is releasing previously taken, now unused gamertags for new players to take/swap for.
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