Since it's pretty certain you're of Irish descent along your paternal line, let me give you most of what you might want to know about the surname "McMahon":
McMahon or MacMahon comes from the Irish "Mac Mathghamba", from "mathghamhqain", meaning "bear". [So MacMahon would be basically "son of the bear"]. The surname arose separately in two areas, in west Clare [seaside county in west central Ireland where my own maternal family stemmed] and in County Monaghan.
In the former, the MacMahons were part of the great tribal grouping, the "Dal gCais", and claim descent from Mahon O'Brien, grandson of Brian Boru [<= great High King of Ireland 1,000 years ago; Irish ancestors don't get any better than this!].
The last Chief of the Name [McMahon] was killed at the Battle of Kinsale in 1602.
The Ulster [northern] McMahons were based in the barony of Truagh in the north of County Monaghan, and ruled the kingdom of Oriel between the 13th and 16th centuries. Their last chief, Hugh McMahon, was beheaded by the [slimy, cowardly] English in 1641.
Today, altho widespread throughout Ireland, McMahon remains most common in the two ancestral homelands of Clare and Monaghan.
Hope that helps, Miss M. If you've got any recent family members' names and would like to see if any other McMahons can provide you info over the Net, go to www.genforum.com That's a site that contains hundreds of message boards for people seeking info on various surnames. Look for either "McMahon" or "MacMahon" -- the difference in spelling is almost arbitrary and it's the same name either way.
From what I've seen, the people who post on genforum are universally friendly and helpful. If you tell them your situation and give them what family info you have, someone's bound to help you dig deeper.
Best of luck to you, Miss MacMahon! God Bless, and don't stop asking questions of your foster parents or whoever else might know something. And come back to see us if you think we might be of assistance.