Well my first suggestion isn't about "hoping" that they'll produce your passport with your desired name, my suggestion is this: Go to the vital statistics office and find out how to get your birth certificate corrected! It doesn't matter that you've got IDs with your desired spelling because I can almost garauntee you that somewhere down the road, some gov't wonk is going to see the misspelling and create a huge hassle for you! My dad went through all his life using "Jones" as his last name. It wasn't until he was getting investigated by the FBI for his first TS clearance that they caught it...Jones isn't the name on his birth certificate!

Actually, he was surprised that he even had one filed, they weren't exactly up on paperwork back then in rural Texas. Which is evidenced by the fact that his birth certificate was filed when he was 2 or 3! Anyway, since everything was done with "Jones" they left it alone. He got out of the military and went to work for Lockheed. He was at Skunk Works and if you know anything about that place, that tells you the types of clearances he held. For those that don't know...it's simple, even the janitors had to have at least a Secret clearance!
He retired from Lockheed and went down to Social Security to get ready for filing to collect from them. Guess what? They wanted his birth certificate!

DD-214 military discharge papers, US Armed Forces ID card, VA disability certification paperwork...all of it useless--birth certificate or no claim! Oh, b/c isn't in the name he'd been using he
entire life? Well, then change the b/c! So yes, he paid a lawyer some $300 I think, took an ad out in the newspaper (part of the process) and got a legal name "change" to the name he'd been using all along. The court sent an order to Texas which then updated his birth certificate to reflect his "new" name.
The upside is not only can he collect his SS money, but he can also now get a passport!

He didn't need one for his overseas assignments, he traveled on his US military ID.
Yes, every state issues a state ID for people who don't/can't drive or otherwise qualify for a DL. The documentation requirements for getting a state ID are pretty much the same as for getting a DL (because many states like CO require their state-issued ID for getting state benefits). Some states will issue both (CA used to issue both to one person but the DL/ID numbers were the same, TX issues both and the DL/ID numbers are different--I still have my TX ID card and haven't lived there in over 10 years). However, many states only issue one or the other.
As for the short form of your b/c. If your current one doesn't have a seal on it, how about getting a current one?
http://www.scdhec.net/administration/vr/birth.htm
"The State Office of Vital Records located at DHEC, 2600 Bull Street, Columbia, South Carolina issues different types of birth certifications: (1) a short form certification (birth card) and (2) Computer-generated long form. The birth card is a wallet-size certification that contains the birth certificate number, the name of the person whose certificate is being issued, the date of birth, sex, the county of birth, and the date the birth was filed. The computer-generated long form contains the following information: 1) State File Number, 2) Name of Registrant, 3) Date of Birth, 4) County of Birth, 5) Father's Name (if listed on the original birth certificate), 6) Mother's Maiden Name, 7)Date Record Filed, and 8) Date Issued. The computer-generated long forms can ONLY be issued at the State Office location – DHEC, 2600 Bull Street, Columbia, South Carolina 29201. "
Note that SC isn't the only state to do this short form/long form deal. CA is one...but the CA short for IS NOT sufficient for State Dept to issue a passport! I was born before the short/long form business so that's moot for me. If you get a new birth card, it'll have a state (or county) seal and would be okay for getting a passport.
"Each of South Carolina's forty-six (46) counties has a vital records office in the county health department. In 2000, the Statewide Birth Certification Project was completed and allows all forty-six (46) county vital records' offices to issue short form certifications (birth cards) for any South Carolina birth, regardless of the county of birth. Statewide birth certification allows a customer (if entitled) to obtain a birth card from any county health department regardless of where in South Carolina the birth occurred."