How to select two columns as one?

You’re looking for the CONCAT function.

mysql_query("SELECT CONCAT(first_name, last_name) As name FROM people WHERE (CONCAT(first_name, last_name) LIKE '%" . $term . "%')");

or even…

mysql_query("SELECT CONCAT(first_name, ' ', last_name) As name FROM people WHERE (CONCAT(first_name, ' ', last_name) LIKE '%" . $term . "%')");

I couldn’t explain you the reasons behind this (…but maybe someone can leave a comment?), but you can’t use the name alias to search for both fields, you have to explicitly CONCAT again.