On Ancestry Library there are three Melodys in the 1850 US census, the first where all residents were listed by name.
The oldest one, Melody Loveland, the wife of Aaron Loveland, was born in Connecticut around 1795. I checked the 1860 census and found the same family. They were living in Wisconsin in 1850 and had moved back east to Ohio in 1860, but the unusual names and ages involved (a son named Miller who was 4 in 1850 and 14 in 1860, for example) show this is the same family. So we can be reasonably sure that Mrs. Loveland really was called Melody.
We can't be 100% sure she was born as a Melody because even back then some people did change their names or become known mostly by a nickname. But it's probable Melody was the name her parents gave her.
This was a very rare name in the 19th century, though. I don't have time to check the original records to make sure, but the number of Melodys in the indexes to the US censuses between 1850 and 1930, the last one available, is as follows:
1850: 3 1860: 11 1870: 14 1880: 11 1890 -- the census records for this year were accidentally destroyed 1900: 67 1910: 47 1920: 95 1930: 122