It's probably neither here nor there, but the only time it is spelt Ludwig (from what I remember) is in the Servant Files which Maxis wrote/programmed himself. The CIA/Majestic 12 people didn't make it, they only accessed the "Datenbediensteter" (translated: DATA SERVANT). Then again, it does say that it's been translated from its original German.
Either way, who really cares. It's just Treyarch laziness with the spelling of a major characters name.
Edit - I made a topic a while ago questioning if Maxis was really German based on Richtofen saying "Stupid Maxis & his stupid accent". A lot of the same arguments are in that thread too.
http://www.callofdutyzombies.com/forum/index.php/topic/149904-is-dr-maxis-really-german/
Well....the accent thing can be given a free pass considering they ARE Germans.....yet they always speak English ....so......Yeah theres that.