In the February 15, 1910, Remington price list the gun is called the Model 1908. In 1911, Marcellus Hartley Dodge combined his arms and his ammunition companies as Remington Arms -- Union Metallic Cartridge Co., and the gun became known as the Model No. 10. During WW-I time the company name got Inc. added. In 1920, the company name was changed again to Remington Arms Co., Inc.
The old factory ledger from Ilion that was started with the resumption of civilian arms production after WW-I, shows the first entry for Model 10 had reached serial number 172939 on Sept. 30, 1919. U was a Remington "stock letter" for this pump gun. So, What is the company name on your gun? Remington Arms Co.? Remington Arms - Union Metallic Cartridge Co.? Remington Arms - Union Metallic Cartridge Co., Inc.? Or, Remington Arms Co., Inc.?
The guns are fine as long as they work, but there doesn't seem to be anyone left alive who can make one right once it gets out of whack.
There is virtually no interest or market demand for these old pumps unless in absolute mint condition or one of the higher grade hand engraved guns. Most average used Model 10 "Standard" Grades sell for $150 or less.