I just closed a Fannie Mae deal with a buyer who wanted to add his wife on the offer after writing and acceptance but before the closing. Basically, the request was made a day after offer acceptance. I was told by the listing agent that Fannie Mae would not allow that once the offer info was inputed into Fannie Mae's system. The way he explained is it just basically boils down to dealing with a govenment entity and all the bureaucracy that goes with it.
Your situation is even more complicated because you have an auction company to deal with. Even if Fannie Mae would allow you to switch names, the auction company is some times difficult to deal with in that regard. I've bought two properties through Willams and Williams with a partner. I attended the auctions, my partner did not. One property I was able to add him after the fact, on the second, no dice. Neither of those were Fannie Mae properties and both were cash deals.
Even worse, you're now looking to buy with an FHA loan.
So, Fannie Mae won't allow you to do a name change, and even if you could, the auction company represents a challenge to do so. The third strike, you are obtaining an FHA loan which will pretty much rule out a double close.
Your best bet would be to try J Scott's advice of talking with either the contact your are dealing with at the auction company, the original listing agent of the property before it went to auction, or even try the title company once they are assigned. Be very nice but explain to them this is not a favor but rather a requirement to close from the lender. Otherwise, close with the hard money lender and refi into your FHA loan when it is permitted. Good luck.