I understand that character migration and transfers are very cool and helpful but blizzard got in my way on this one. To change my name costs money if you have done it once already and that can be annoying to players that have to change there name to migrate a character.I don't want to spend $10 so i can change my name and it might not even work. i hope that Bungie can change how you migrate characters because i don't want to spend money on a name.
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it is just cross save, so you will be able to play the characters on whichever platform. You will still need a platform account and the game on that platform to do it. So your console "name" is not transferring to the pc. Also keep in mind when the cross save is enabled we will be on steam not blizzard.