He's listed as William T. Fallowell age 22 on his 7th Inf service card in 1861 but as William P. Fallowell 26 on the 11th Inf card in 1864.
There's a Wm. P. Followell 31 born KY in Louisiana, MO 1870, a machinest with a wife Mary 19 and son John 7/12, but I can't identify him in earlier or later censuses.