How can I find out my grandpa's real name?

When did he arrive and where is "here"? We can assume the U.S., but is is an international site.

Immigrants to the U.S. did change their names occasionally, but the family legends of this happening are far more prevalent than their reality. What makes you think it was changed if you don't know what it was changed from?

It may have been spelled a little differently over time after arrival. Be sure to check various spellings. Spelling wasn't standardized until fairly recently and clerks would spell the same sounding name however they thought it should be. (I have 1 immigration document with 3 spellings...on the same document).

If he arrived in Ellis Island, or a few of the other ports during the same era, the name change would have occurred after his arrival, not at Ellis Island or the port. Shipping companies were required to pay passage back to Europe for any passengers without documentation. this meant they did a splendid job making sure everyone on board had papers and was who they said they were. The port hired many translators and officials to check and verify paperwork. So the first order of business is to find evidence of a legal name change in the U.S. A legal name change would have occurred in a county court where he lived or with his immigration and naturalization papers. NARA can help you track down where the immigration and naturalization papers would be based on where and when he arrived/lived in the U.S.

http://www.archives.gov/

You might also check with Cyndi's List for helpful links: http://www.cyndislist.com/immigration/