Ping is Apple’s new social network for music.
In iTunes, bring up Ping and edit your profile. You can change your first/last name there.
Unfortunately, the caption there explains that the name you provide is associated with your billing information. So, if you change your name to something like “Rocky Bullwinkle”, then any future purchases you attempt to make in iTunes might fail because it will attempt to authenticate your credit card with this new name.
But heck, it won’t hurt to try it. If you find you cannot purchase music, then change your name back.
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Besides, it’s not like Ping is all that social right now anyway, with no integration to major social sites like Facebook, Twitter, etc. You probably wouldn’t miss much if you disabled Ping in iTunes altogether.