Assuming you won't cause your wife/husband/parents to freak out if they see another name on your credit card statement,
I bank with Bank of America and have a Visa through them as well. I asked last year if it were possible to do this, and people weren't sure. Well, I checked my bank's website, and the option to add an authorized user through an online form has been restored.
My plan was to knock out orchiectomy and legal name change at the same time, but I've been fighting with the whole standards of care thing and have been delayed considerably (and funding has been hit or miss.) Anyway,
No birthday/social/etc required, just the name as you want it on the card, and "relation: other" checked. Got the card in the mail today. Called in to activate it; when the nice lady on the phone asked if I was the card holder or the other authorized user calling in on behalf of them I said "I'm both, I'm having a sex change and it's not safe for me to use a man's credit card."
And they were totally okay with that.
A signed visa cannot be rejected, and you may not ask for identification except when buying alcohol. I wasn't going to throw a bitchfit when it was a man's card held by a woman, but now that it has a woman's name on it, and tomorrow I will go down to my bank to have them add my (updated) photograph to the card, I will absolutely rip the face off of any clerk or manager that demands my ID.

Of course I'm going to keep the male named card with me at all times (also with my photo ID on it), but hopefully I won't need to use it.