I will give a hypothetical example to explain my question.
Assume we have N people (N unknown). These people are standing in a line to pass through a gate one by one. The gatekeeper will decide to send each person passing by to be questioned with a known fixed probability p (i.e., he will generate a uniform random number, $u$, and if $u<$p he will send that person for questioning).
At the end of this process, you will come in to the room where all selected people are gathered. You count how many they are. They are M of them.
In this situation the total number of people N is unknown.
It's intuitive that an unbiased estimate of the total number of people N is: $\hat{N}=\frac{M}{p}$.
My question is what is the $Var(\hat{N})$ ?
You're just dividing by the constant $p$, so the variance is $\frac1{p^2}$ times the variance of $M$:
$$ \operatorname{Var}\hat N=\frac1{p^2}\operatorname{Var}M=\frac{np(1-p)}{p^2}=\frac{n(1-p)}p\;. $$
I took the liberty of adjusting the capitalization to the usual conventions. I'm not sure what you mean when you say that $n$ is a random variable; as far as I can tell it's a fixed unknown parameter.