Welcome to the Wefugees Community and thank you for sharing your question.
In Germany, you can not "register" a partnership anymore - you would need to marry in order to formalise your relationship and to obtain the family status. Please see this website for more information. Are you sure that your partner does not hold a Duldung at least? If he is staying "illegally" in Germany, please be aware that the registry office (Standesamt) may report him to the police or immigration office as soon as you get in contact with it. Marrying while holding a Duldung is possible though. Please see, for instance, this thread on this topic.
I am not very familiar with the Dutch regaulations and procedures, but I read here about the registered partnership in the Netherlands. I am afraid, however, that your partner will need to apply for a visa before being able to cross the border legally. Since he is not holding a residence permit in Germany, he is also not allowed to travel freely (usually for up to 90 days) within the EU.
Maybe you can get in touch with a migration counselling office to discuss your situation in more detail. Please let us know if you need support in finding respective services in your area.
I will also link our dear @mbeon-Ruth and @mbeon-fardeen here. Do you agree on my explanations and/or is there anything you would like to add?
In any case, don't hesitate to get back to us with any further questions.
All the best,