The Jarvis Pennyworth of the New 52/Prime Earth continuity likely 'inherited' his first name (out of universe) from Jarvis Beagle, the father of Batman's butler in the Golden Age/Earth-Two continuity, Alfred Beagle.
I couldn't tell you why Jarvis Beagle was given the first name 'Jarvis,' but that's not what you asked, and we can safely rule out the notion that the name was inspired by the Marvel character, Edwin Jarvis, since Jarvis Beagle was first mentioned in Batman Vol. 1 #16 in 1943, 21 years before Edwin Jarvis was introduced.
ALFRED BEAGLE: You may remember my father, Jarvis, who was your father's butler for many years! The poor old gentleman was heartbroken when I forsook the family calling to be an actor in the music halls!
Batman Vol. 1 #16 (May, 1943)