CPR registration

Hello everyone, as I mentioned in a previous post made a few weeks ago on this forum I'm moving to CPH with my girlfriend at the end of January for university. The only problem that we are encountering is that concerning the rent.
During the first semester we want to limit the expenses of rent as much as possible because there are other expenses like books, bikes etc so we thought that it would be more appropriate to live in a rented room during the first semester and then starting the 2nd semester try to get an apartment on our own. I registred on boligportal.dk and talked to some landlords and the majority of them told me that even though we could stay in two in a room it is not possible to register more than one person for CPR number, additionally I asked if it is a law or something that the landlord decides and I've been told that it's a law.
It seems weird that there is a law stating how many people can register for a CPR number in a household.
Can you tell me if it is true or only something that landlords typically say? And if it's true what would be the solution? Time is running out, we already booked the flight and confirmed our places at university but finding a place to stay seems impossible.

Thank you all in advance for the answer. Have a great new year.