Can a state trooper pull me over for no reason and search my vehicle?

I was on my way home in the early am. The other night and I had just pulled off the on ramp onto the highway when I saw the lights. I began to pull over when they pulled behind me and turned the lights off and right there didn’t seem right. They approached my car as normally everyone does. I asked why I was pulled over. He told me that they were doing a routine search. They never asked me for my license or registration. As I became more aware of how awkward this stop was going, I looked for their name tags neither cops had one. I asked their names and refused to tell me. They never asked me to get out of my car they simply said to me this is a routine search get out and put your hands on the hood. After an hour or so tearing my car apart they decided they weren’t going to find anything and let me go. I sat and waited for them to pull out so I could get the licence plate number but they didn’t. After so long of that, I just wanted to get out of there so I pulled out. They immediately followed me. I drove below the speed limit in hopes again that they would pass and I could get their plate but they never passed me. I finally got to my exit and went home. A few things just didn’t feel right about what had happened. Can they pull me over for no reason and tell me they are searching my car? Can they go without wearing their name tags? Don’t they usually keep their lights on the entire time of the stop?