Schneider's Saddlery does jackets with embroidery. I'd "google" unisex coat/custom embroidery and see what pops up. Also you might find the coat you want at Old Navy or such and then just get the embroidery done on it. finding the coat will be the most difficult thing IMO---check Ebay also
I used to work for a huge h/j barn in upstate NY, and all their staff got monogrammed everything. They used LL Bean. It's been 4 years since I worked there, and the coat/jacket/turtle necks/everything else they gave us are still my go to when it gets cold! It has a fleece liner that zips in/out. My ONLY beef is that it has a different farm logo and that it's only water resistant.