If my name is on a deed at the court house for a piece of land (in WV) and someone else claims it because they mowed the land for years, who is right?

The specific topic this involves is known as "adverse possession."  As for whether or nor the other party can establish adverse possession depends on several factors.  Generally speaking, adverse possession requires a "hostile / adverse claim, actual possession, and exclusive, open and notorious possession of the property. You should speak with an attorney in West Virginia who practices in that area of law for a more detailed analysis. Best of luck.