It is called a mixing valve. You will have an extremely difficult job to replace it through that small access. The valve in the picture had female threads. Someone installed male adapters and then soldered the copper to those adapters.
Does your new model have threads, male or female? If yours has male threads, you can use female adapters and solder to them, or you can insert the copper right into the valve body and solder direct . Obviously, in all cases, you will remove all internal parts of the valve prior to soldering on or near.
The existing valve is not a beautiful example of a good solder job, but apparently lasted all these years.