George, Unable to ascertain his correct surname spelling. It could have and probably was spelled a myriad of ways.
In my opinion based on your information, fold3 has him (spelled) as M. McIchenny of Company B 3rd Mississippi Infantry but only has one page of Compiled Military Service Records as follows.

A Company Muster Roll within his Compiled Military Service Records dated September 29, 1861 stated Private M. (Spelled as) Mclchenny of Captain W. H. Morgan’s Company (Sunflower Dispersers) 3rd Regiment Mississippi Volunteers was mustered into service on September 29, 1861 at Camp Clark in Bay St. Louis, Mississippi.

A notation at the bottom of the page stated “This Company was successively designated as Captain Morgan’s Company (Old) Company E and (New) Company B 3rd Regiment Mississippi Infantry.”

There are some hits on fold3 at miscellaneous under (Spelled as) Mortimer Mcllhenry as an example. May or may not be the same man? There are other hits under the spelling of Mclhenry on miscellaneous but only one hit in Company B of the 3rd Regiment Mississippi Infantry.

This was a specific search and should not be regarded as all inclusive.

Hope this helps, time to get back to Camp Chase.