I'm trying to setup a wordpress blog,
but apperantly the database name can't be over 16 letters or wordpress won't work.

And my website name (counterproductions) is already longer that 16 letters...
Is it possible to make a database without the "counterproductions\_" in front of the name?

Afraid not, what you can do is create a new user and just use the details for that database within your current domain.