Checking various sources, the original surname appears to have been German (or German-Swiss):  MESMER / MESSMER.

1.  Liahona Research (Orem, UT), compilers.  1996. Marriage Index:  Ohio, 1789-1850.  (Broderbund CD-400):

Mesamore, George

Corbin, Martha

16 May 1844

Hancock Co.

2.  Family Quest Archives:  Ohio Federal Census 1850: Hancock and Hardin Counties.  Heritage Quest CD M432-692:  Amanda Twp., Dist. No. 48, Hancock Co., OH, p. 462B-463A, 42/42, enumerated 5 Sep 1850 (extracted by Diana Gale Matthiesen):

Sarah Philips	45	f			Pa
George Mesemore	25	m			O
Mary	24	f
Peter	22	m	laborer
Jonas	21	m	laborer
Zachariah	14	m
Daniel	13	m
Jacob	12	m
Barbara A	10	f
Henry Green	26	m	laborer
[next page]
Eliza Jane Green	23	f			O

It's very hard to figure what's going on here.  Is this George MESEMORE really our subject?  Has Martha died?  If Sarah is the mother, why is her surname PHILIPS and the children surnamed MESEMORE?  This enumerator certainly wasn't wasting any ink.  Listed five households from Samuel & Rebecca HOYER, who are listed two households from William & Maria HOYER.  There was a Caroline HOYER who married Thomas STRAUB. 

3.  Broderbund.  World Family Trees.  Vol. 40, Pedigree No. 356.