Three kinds of police departments in the State of Nevada.
1) Those police departments in each city. Some smaller towns have none, rely on
2) County Sheriffs. Each county has its own sheriff department. Then there is the
3) State Department of Public Safety, which includes the Nevada State Police and the Nevada State Highway Patrol.
I don't know if they have a nickname peculiar to Nevadans. My guess is the Highway Patrol guys might be referred to as NHP (similar to how in California the highway patrol is CHP [or CHiPs as in the old TV series of the same name--have no idea if the Nevada Highway Patrol are called NiHPs, but they should be

]). I found this information in
Google. And I did that for a story I was writing (and have completed since--just) that involved both the Nevada Highway Patrol and the Las Vegas Police Department (in the mid 1950s, no less).
I live in Oregon (neighboring state) and our system is almost identical. We call the Oregon State Police just that: State Police. Whatever county you're in, in Oregon, you call the County Sheriff the County Sheriff or just "the Sheriff". Most of the officers in any County's Sheriff department are "deputies" but I wouldn't ordinarily call one that in a casual conversation, and maybe not even to his face. He's with the Sheriff's department, he's the "Sheriff."