Whitlam is an English surname from Middle English forms of the words "white lamb." It is uncertain why this became a surname; it could originally have been a nickname for an inoffensive or mild-mannered person, or it may have originally been a "house name" from a house marked with a sign featuring a white lamb, during the time before house numbering systems were invented.
This information is from Hanks & Hodges's
A Dictionary of Surnames, verified by Reaney &
Wilson's
A Dictionary of English Surnames.