I know that Dwight D. Eisenhower was the supreme commander of the allied forces, my question is if he had a Axis counterpart.
Hitler. Well not really of course. But he appointed himself Commander-in-Chief of the german Army in 1941. But he never had official authority of forces of other axis nations and also the position he gave himself wasn't really comparable to Eisenhower anyway.
Eisenhower was supreme commander of the allied expeditionary forces. This meant all the lead up to the normandy landings, D-Day itself, market garden, battle of the bulge and most of the war in 1945. He still reported to the Combined chiefs of staff (both US and British joint chiefs of staff).
Eisnhower was not in command of allied forces in the medeterrainian theatre, including Italy. The invasion of southern france was also out of his command for about a month until the two invasions had linked up.
He was also not in command of the pacific theatre or the russian theatre. And then depending on your definition of "allied powers" the chinese/vietnamese/thai theatres were also out of his command.
So just like Eisenhower wasn't in charge of all forces there was no one supreme commander of the axis forces, but there were field marshalls in command of theatres similar to Eisenhower. Erwin rommel was in command of the atlantic wall defence during the normandy landings for instance.