How do you find a soldier in the 7th Infantry Company B?

Clarification

Instead of 7th Infantry Company, you probably mean 7th Infantry Regiment. Soldiers usually referred to their regiment or occassionally their Division. The discharge papers usually refer to the veteran's regiment.
During WW2, the typical Infantry Division consisted of 3 Infantry Regiments and 4 artillery battalions and an engineer battalion and other supporting companies. Each Regiment consisted of 12 companies divided into 3 Battalions as follows:
1st Battalion - Companies A, B, C, D
2nd Battalion - Companies E, F, G, H and
3rd Battalion - Companies I, K, L, M (no J).
So, the term "7th Infantry Company" is not correct. A soldier would refer to his unit as:
"Company B, 7th Infantry Regiment"
If the soldier was talking to another soldier within the same division or location, he might shorten it to say: "7th Infantry, Company B". Here he implies a regiment and the comma(,) seperates the two levels of command. So your Question is not really Incorrect, but it needed some clarification for some readers.
Also, Company B was in the 1st Battalion, so any reference to "1st Battalion, 7th Infantry Regiment" would include his company. The Battalion was commanded by a Colonel and is the basic unit used in combat. So many histories will refer to the battalions and not the companies.  

Answer

The 7th Infantry Regiment was part of the 3rd Infantry Division. This unit saw combat in Italy and fought at Anzio until July 1944 and then landed in Southern France in Aug 1944.
There is a unit history on the 3rd Infantry Division that was printed in 1947 or so. Recently, it has been re-printed by Battery Press. It is a very large book and it is unique to most unit histories in that it contains an extensive roster of the soldiers who served in this unit. I would recommend that you contact your library and ask for an inter-library loan for this book. This book may have his name in it.
The 7th Infantry Regiment were known as the "Cotton Balers". This unit is a descendant of a unit that fought at the Battle of New Orleans in the War of 1812 and they used cotton bales to fortify their position.
I wouldn't mind looking through it for your soldier's name.
Custermen
Reference: "History of the 3rd Infantry Division in WW2" by Donald G. Taggart, available through Battery Press in Nashville, TN.