Just to throw in my 2 cents worth. "ig" would sound like "ik" in German. The early census takers were "English" and the German pioneers only knew how to spell their names in German resulting in some interesting spellings.
Hannover would be the Kingdom of Hannover which at one time, like almost everything else in Germany, belonged to Prussia. The immigrants would sometimes say Hannover and others Prussia. When they became citizens they would have had to renounce their allegience to the King of Prussia. Emigrants from that area usually left from Bremen but later Hamburg became popular. That area is now known as Niedersachsen or Lower Saxony.
Normally I would suggest you get church records from the LDS but they have almost nothing on Hannover.