Since this is really a legal issue I'd consult the attorney at the title company (the one drawing up the deed), to see what they require. Short answer: the names should match; you'll need an addendum to the agreement.
(Side note: are you under agreement at all? Is it day 15 since the offer, or since the agreement was fully executed and you went under contract? If you're negotiating repairs, make sure you're within the inspection period, especially with no other contingencies, or you'll end up buying it as is.)
Is there a "human" seller, or is it a foreclosure? If it's bank-owned, the bank may have special provisions about assignments (generally frowned upon, since sometimes they're "flopping" schemes).
In any case you'll need an amendment to the agreement. I just did one of these recently to add a buyer's wife to the contract (since she was going to be on the deed as well).
The name on the deed does indicate ownership, but it might not be the whole story. For instance, in the example above where a buyer added his wife to the deed, she would have had a spousal interest in the property whether she'd been named on the deed or not, due to the marriage.
(Side note again: to avoid future title issues, I always recommend putting everyone who has an interest in the property on the deed. I had a case once where it was impractical to have the wife sign everything. The marriage was disclosed on the agreement (e.g., "John Smith, a married person"), and the husband got a power of attorney to sign for his wife. Contrary to popular belief, husbands and wives can't legally sign for each other just by virtue of being married.)
In practice, title companies aren't always too upset about married couples not dotting all the i's and crossing all the t's, since the legal marriage sort of makes it all come out in the wash anyway. But non-married family members (not to mention unrelated business partners) get more scrutiny, and really should be done correctly to avoid legal/tax issues later.
There are four separate things: the sales agreement (contract), the note (loan), the deed (ownership of the property), and the mortgage (securing the loan by the property). The note and deed can have different names (e.g., two can have ownership, but only one be responsible for the loan), but the contract should match the deed. Since you're cash buyers, in this case all you have is a contract and a deed.