You will create a brand new 10-digit login under http://att.com/mygophone where you will feed the new SIM. It is entirely a new account, with no sharing of balances between old and new -- like "ships in the night."
No Sharing of Balance:
Because balances are not shared, you will have use of the old SIM until you drain the account to zero, and then just flip to the new SIM if you use option (2). Not sure what the retail store will do under option (1), other than probably just cancel your SIM and close your old account and balance.
I would go with option (2). Others may add to this with their own preferences/options. But be assured that, regardless, you can use your existing phone with a new number -- no problem.
Re: PREPAID: CAN I CHANGE MY PHONE NUMBER AND KEEP EXISTING PHONE???????
Depending on the reason why you'd like a new phone number, I would suggest a couple of additional options -
1) If it's due to phone calls/texts, etc. you are getting on the phone number that you received (for a prior owner of the phone number), I would contact customer service and request a different phone number. I believe they can re-provision one over the air if you are receiving a large volume of unwanted (annoying and potentially chargeable) activity because the number was recycled too quickly.
2) If you just want another phone number/SIM card, AFAIK your local at&t Corporate store will provide you with one at no charge if you'll add funds to the new GoPhone account while you are in the store. Just tell them that you are going to use it with your existing phone rather than buying a GoPhone package.
=^..^= There must be a happy medium somewhere between being totally informed and blissfully unaware.