It means he’s married, engaged, or has a girlfriend. There are few more obvious signs of a cheater than a guy who won’t share basic personal information.
Why else wouldn’t he give you his phone number? He’s not playing hard to get– he doesn’t want you to call because his wife might see the number on his caller ID and get suspicious. And he won’t tell you where he lives because there is another woman living there and she isn’t his roommate.
He only calls you at work because he has something to hide. Does he always call from his work number? Assuming his wife isn’t also his boss, she won’t be checking his phone records at work.
Honestly, unless he’s a spy or in the witness protection program, he’s attached and looking to cheat. He’s carrying on a secret life. Why do you want to be a part of it?