I agree that if you can, SELECT COUNT(name) WHERE ... works best. Also, depending on whether or not the NAME column is a primary key or otherwise unique value, you may want SELECT COUNT (DISTINCT name) WHERE ... to get a count of all the guaranteed unique names. But if for some reason you can't or you don't want to, you can use this snippet after your original query:

my $rows = $sth->fetchall_arrayref()
my $num_rows = scalar (@$rows);
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It will return a reference to an AoA (Array of Arrays). The scalar is optional, of course. You can then use the data in $rows for actual manipulation, if the need arises...

MM