It's not impossible to have two names on the deed to your house but only one name on the mortgage. It's not a slam-dunk either: You'll need your mortgage lender's approval, and the lender may not bite. If it does agree, it may require the non-paying owner to sign an agreement guaranteeing the lender's right to foreclose.
Normally, co-ownership enables you to pool your resources and get a better deal on a house. If you're going it alone, you have to be able to afford a house solo. The industry rule of thumb is that your house payment shouldn't exceed 28 percent of your gross monthly income: If you're the only name on the mortgage, that's 28 percent of your income alone. You'll also need excellent credit.
Your mortgage lender may be more amenable if you show that it's not practical for both you and your co-owner to go on the mortgage. For example, your co-owner may have such dreadful credit scores that taking out a mortgage isn't really an option. He might be unemployed, or self-employed with unpredictable income, so adding him won't help you get a better deal. If you qualify for a first-time homebuyer credit and your co-buyer doesn't, that's another good reason.
If you can't find a lender willing to put one name on the mortgage and two on the deed, one alternative is to put the same single name on both. That may simplify things with the lender, but it has its own risks. If you're not married, the legal owner can sell the house and keep the money or kick the other partner out.
If you intend to add your co-owner's name to the deed after the loan has gone through, your mortgage lender may have objections. Adding the name means you transfer title from yourself alone to you and the co-owner -- and transferring title could trigger a due-on-sale clause in the mortgage, requiring you to pay it off immediately. Sound out your lender before you do anything that could come back and bite you.