Yes, but DO NOT give that compressor to a rebuilder with your tag; carefully REMOVE THE TAG. It is secured by two tiny nuts that thread onto tiny studs. Specify that they CANNOT switch compressor cores on you! Take closeup photos of all casting characteristics and document your compressor; and tell them you have done so. Specify that they cannot put any of their own ID markings on the rebuild.
My nut driver set happened to have the correct size socket--size not available right now-sorry. Use a thin layer of tape, or plastic (sandwich baggie) around/over the nut so your socket does not make a witness mark on that tag surface.
Oh, and specify that all original hardware (fasteners) be re-used--no replacements--because of markings and type.