Yes, they did. There are numerous vouchers in the archives, some on their own elegant letterhead and some printed arsenal receipts, all titled "Union Manufacturing Company." But LOCALLY the people called them, "Sloat's." Apparently the fellow that patented the sewing machine was named, Sloat, and Union Mfg. advertized it as "Sloat's improved shuttle..." Soon everyone just called the factory, Sloat's. When they started CS gov. contract work, one such contract was the repair and conversion of rifles/muskets. Soon the locals started calling it, "Sloat's Gun Factory." That name stuck for a long while.

In fact, proprietor James Kent went by the nickname, Sloat, and signed official CS receipts, Sloat.

Sorry if this is all a bit off-topic, though someone may have seen a document somewhere referring to Sloat's and not known the origin.