My wife kept her maiden name and added my last name with no hyphen. So she has 2 given names and 2 last names on all documents in both Brazil and the US. After getting married in The States, she legally had to change every Brazilian document to coincide with the new name.

To answer your question, you should always put the names exactly like they show on the passport. If the passport, green card, visa, whatever, shows 2 last names you need to put 2 last names.