Reading some papers about neutron stars, I found that some astronomers measured the frequency of a pulsar, which is a sort of lighthouse. My question is if the measured pulsar frequency is the same as the frequency of rotation of the associated neutron star.
You are asking whether the frequency (and you mean periodicity) of the pulses coming from the pulsar are coinciding with the frequency of the rotation of the star itself.
Let's take for example J0437-4715, it rotates every 5.75 milliseconds.
For example, J0437-4715 has a period of 0.005757451936712637 s with an error of 1.7×10−17 s. This stability allows millisecond pulsars to be used in establishing ephemeris time or in building pulsar clocks.
This millisecond pulsar rotates about its axis every 173.7 seconds, and yes, the answer to your question is in this case.
It emits a searchlight-like radio beam that sweeps past the Earth each time it rotates.
So the question in this case is yes, but please note that it might depend whether the rotation of axis is coinciding with the magnetic axis.
If the axis of rotation of the neutron star is different to the magnetic axis, external viewers will only see these beams of radiation whenever the magnetic axis point towards them during the neutron star rotation. Therefore, periodic pulses are observed, at the same rate as the rotation of the neutron star.
There are many types of neutron stars, and some are magnetars, pulsars or both.