You have the daunting task of trying to single out a man with a most common name. You have some tools available that might help you narrow things down. This site:
http://humphreys1625.homestead.com/UnitIndex.html will provide you a list of units that were assembled, some completely and some partially, from Pontotoc County. This site: http://www.itd.nps.gov/cwss/ will provide a not quite complete list of soldiers that served from Mississippi. (By limiting your search to any Johnson with the first initial W from Mississippi, you will find 3 W Johnsons, 6 W M Johnsons, 29 William Johnsons, and 1 William M Johnson.) The last one could be your man - he was in the 27th Inf. Regiment, Company C "Fredonia Hards".
But without cross matching and eliminating the others, you can not be sure that is him. To complicate matters more, he could have enlisted with friends in a neighboring county, or, if he had only been in Mississippi a little while, he may have gone back to Alabama to enlist with friends from his old neighborhood. He could have even been conscripted, and ended up in a unit from another part of the state altogether. His name could even have been mistakenly recorded as Johnston! However, after going through all of these men and units, if you do think you have narrowed it down to one or two men, you can order their service files here on the board by clicking the link at the top of the page. You might then have enough evidence to lock in on one person. Good luck in your quest.