Have a look at the MySQL manual, read about the "IF" clause.
You can build an IF clause to return a surtain value, based on wether or not
something matches, like:
SELECT IF(Name="Name",1,2);
This returns 1 if Name="Name", and 2 if Name does not equal "Name".
You can put these IF statements in the ORDER BY or GROUP BY clause (or even inside other IF statemenets) to arrange your answers.
SELECT * FROM table ORDER BY IF(Name="Name",1,2);
this will return the rows where Name="Name" first, followed by the rows where Name is something else.
Be carefull, this can be a very expensive (read: slow) operation to perform,
so make sure you have the proper indexes etc.