You normally should create only the constraint, unless you need something special from its index. For example, if you always use ORDER BY GS_PAYS_LIB DESC in your queries it would be better to create a unique index with the descending order before creation of the constraint. The constraint will be able to use that index too instead of creation of own one (with default ascending order).
I just informed you that you read the name of internal indes from somewhere; it wasn't the name of your constraint. Constraints and indexes are different things and information about them are reported in different places.
Usage of unique indexes instead of unique constraints is usually a bad idea. Indexes normally should only be used to improve efficiency of your queries; they are not standardized and they are not very portable between different DBMS.