What Does the 'C' Stand For in Thomas C Rice?

My father's name is Thomas C. Rice (1929-1983). Our family has always wondered, 'What does the 'C' stand for? Why didn't my father's birth certificate have a full name? Here is an educated guess, with the facts first:

Tom's grandfather's name was Simon C. Rice (1868-1956). I've attached a photo of his gravestone, which is at Stevens Chapel in Mattie, PA (Bedford County, PA). Hmmm,  what does the 'C' stand for?

Tom's great-grandfather's name is Nicholas C. Rice (1836-1918). Hmmm, what does the 'C' stand for? Did Pap name my Dad after Pap's father or grandfather?

Well, looking at the census and other records, Nicholas used his middle name all his life and dropped 'Nicholas' . And his middle name was...Cornelius (see his Civil War Registration, Number 7 on the document, as an example). And Nicholas gave his son the name Simon Cornelius Rice!

So, did Pap and Gram name their son Thomas Cornelius Rice? My educated guess is 'yes'. But why make it only 'C' on his birth certificate? And why did my father never provide any indication that he had the family name 'Cornelius'?

My guess - Gram didn't like the name Cornelius! I cannot yet find that name anywhere in the Pennell family history. I'm guessing Gram reluctantly said 'ok' to Pap, but I'm sure she was in charge of filling out the birth certificate. And I'm willing to strongly suggest that Pap knew Gram didn't like it, and this strong willed couple agreed not to make a big deal of it, and that was the end of 'Cornelius'.

One other note - perhaps Tom found out at some point that C stood for Cornelius, and really didn't like it. So, he too went with the 'C'.

Any other thoughts?