Okay, so:
1 or more letters or digits
Followed by zero or more:
space
followed by 1 or more letters or digits
You still haven't said whether multiple spaces count as "a space", but I'll assume not; so that "This name" is allowed and "This name" is not.
(Please correct me if i'm wrong..)
You are; if you're talking about user input you could get anything. Someone could stick an audio file in that field if they felt like it.
Well, that description above is pretty straightforward.
A letter or digit: [a-z0-9]
One or more letters or digits[a-z0-9]+
A space followed by one or more letters or digits: [a-z0-9]+
Zero or more (space followed by one or more letters or digits): b[/b]
One or more letters or digits, followed by zero or more (space followed by one or more letters or digits): [a-z0-9]+( [a-z0-9]+)
PCRE pattern delimiters for preg_match() and mark case-insensitive:
/[a-z0-9]+( [a-z0-9]+)*/i