The problem is: Information on purchases and sales of property are public record. Anyone can go down to your courthouse and see who bought property, how much they paid, where the property is located, and so on. Again, public record. And that means a newspaper can print that same information. It's not against the law.
On occasion--for example, for certain types of crimes--newspapers will voluntarily withhold the name of the victim. Still, anyone who goes down to the courthouse or police station can get that information.
If you don't want your name and address appearing in the paper, you've got a couple of options. The first one is to ask the newspaper to withhold the information about your transaction. I'm sure many would accommodate your request. Just ask.
The other option is to create an LLC or a land trust and use that in the purchase. Recognize that in either case, your name would still be on the mortgage. But the owner of record would be the LLC or land trust. And that name could be anything you wanted: "The 123 Main Street LLC," for example. Someone could go to the state and look at the LLC records and see who the principals are in the LLC, but all that would appear in the paper would be that "The 123 Main Street LLC" bought 123 Main Street for $100,000. You could even get around the dollar amount if the seller created the LLC (or land trust), then placed the property into it. You, in turn, would purchase the LLC.
Check with a lawyer for more information on how to do that. But it certainly is possible. First, though, I'd suggest just finding out whether the newspaper would be willing to withhold that information.
Hope that helps.