Yes of course you can have your personal info blocked.Every domain name registrar provide this function,mostly are freely.Try to contact with your domain host company if you already have a domain name ask about it.
Hello, to protect your personal information you need a service that is named whois guard, id protect(ion) or privacy protection, there are other names but are all similar with these.
some companies offer the service for free and in anothers you need to pay.
I have created a topic to chose a company that gives me the best price for domain registration/renewals/transfer + privacy protection. And the company I have choosen was name.com. They offer free privacy protection and their price I think was the best. My second choice is namecheap.com, their id protection are paid but it is cheap. I wouldn't go with godaddy.com for their prices, I think they are abusive. BUT, all three companies are well spoken in this forum.