Because most of the police force in US in maintained by local government, like cities or counties. Since laws vary from state to state and cities to cities, it is helpful to mention where the incident is taking place. Mentioning NYPD tells you a lot of things at once- that the incident is specific to New York city (since state and federal authorities were not involved), and that it was done by local police force of New York city, which has very distinct operating pattern and policies from some other police force, like one in LA (the LAPD), or some small rural police force.

As to why LAPD and NYPD are famous, that must be probably because these two cities have incidents that are worth national/international discussion. If you start reading more local US news, they usually mention which police department is involved in the case, like the county head or State attorney, etc.