The name originated with the location of the post office.  It was situated near a grove of Oak trees. The name was originally "Grove Oak" until 1895 when it change to "Groveoak".

The post office was established in 1873 with Jesse P. Horton being the first Postmaster.

Some of the first families to settle in the area were:  Latimer, Manning, Prestley, Summer, Rains, Armstrong, Berry, Bethune, Fossett, Gilbert, Horton, Richey and Smith.