Most residential thermostats are designed to be easily removed on one of two ways:
The entire device slides up ~ 1/2" and then pulls off the mounting screws
The front pulls forward, possibly with a plastic tab or two on top or bottom pried open with a flat screwdriver, revealing a back panel screwed into wall and containing the connections to the wires going to the furnace & air conditioning.
Either way, once you have it off the wall it is usually easy to find manufacturer/model information.
That is a Noma thermostat. It's a pretty junky thermostat. I believe that one pulls straight of the mounting bracket. It may be branded differently than Noma but I recognized it immediately.