The problem these days is that "they all look alike!". This one bears some resemblance to a Glacier Bay or Pegasus from HD. That means globe union, meaning it could also be Danze or Gerber, or many other brands. But those could all use the same cartridge. A photo of the handle and trim plate might also help.
You should not take these things apart, because they are not repairable, and now you might not be able to put it back in temporarily!