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Your John D. Pedersen designed pump gun was introduced to the public in the Remington Arms Co. 1908-09 catalogue as the Remington Repeating Shotgun --
In 1911, Marcellus Hartley Dodge combined his firearms manufacturing company with his ammunition company as Remington Arms - Union Metallic Cartridge Co. and in the Rem-UMC 1911-12 catalogue they began calling this gun the Model No. 10.
Even though Remington Arms Co. didn't introduce these guns to the public until 1908-09, here it is in the hands of professional shooter Frank Riehl holding one in this 25 May 1907 picture --
And, look close at the little sketch in the upper left corner of this page from the 1906 Remington Arms Co. catalogue --