how to get category name if my category got custom slug

See http://codex.wordpress.org/Function_Reference/get_term_by

The following code will work for your situation:

$cat = get_term_by( 'slug', 'aeroplane', 'category');
echo $cat->name;

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)