The apostrophe s ('s) at the end of a noun is the possessive form. A possessive noun indicates that something in the sentence belongs to that noun.
A possessive noun indicates possession, ownership, origin, or purpose.
Examples:
Mitchell's desk is nearest the door. (possession)
Mr. Mitchell's dog is a beagle. (ownership)
I've read Margaret Mitchell's novel "Gone with the Wind". (origin)
Mitchell's Campground is reasonably priced. (purpose)
you put an s, you put an s at the end
Mitchell Construction ended in 1973.
Mitchell Hutchins ended in 1977.
Mitchell S. Buck was born in 1887.
Daniel S. Mitchell was born in 1838.
Daniel S. Mitchell died in 1929.
Mitchell S. Goldberg was born in 1959.
James S. Mitchell was born in 1784.
James S. Mitchell died in 1844.
Olivia S. Mitchell was born in 1953.
Charles S. Mitchell was born on 1856-11-13.
Charles S. Mitchell died on 1922-01-09.