For the definition of the Poisson point process, the N has to be a Poisson random variable with its mean related to the area/size of the simulation region. This is non-negotiable. But if you fix N=n to some natural number (that is, in probability language, you condition on N=n), you then get a binomial point process.
As I remarked in another response, I recently wrote about simulating these two point processes. The binomial point process on a rectangle is detailed here here. The Poisson point process on a rectangle and on a disk.
