Random query on what? By your SQL definition, you're querying a field named "Random" from a table named "database"
To exclude something you could do:
... [SQL] ... WHERE [fieldname] NOT LIKE '$name'
or
... [SQL] ... WHERE [fieldname] <> '$name'
(this is more of an exact match and would be case sensitive)
or
... [SQL] ... WHERE [fieldname] != '$name'
(this is MySQL friendly)
Can we get more details on the field and how your want the random functionality to work?