This family originated in England, perhaps in Shropshire.
The DNA test participant is a descendant of Thomas Gough b. 1791 d. 1841/48 Shropshire, England. A second Gough kit is from the defunct Ancestry YDNA product and is a 31/32 match to the Thomas Gough descendant. Unfortunately, the Ancestry YDNA participant has not provided his family tree. The FTDNA participant did not recognize the name of the Ancestry participant, so the two YDNA participants are seemingly not closely related. Without a clear view into the nature of this match, it is uncertain if the two men connect in the 19th century, 18th century or prior.
Curiously, the FTDNA participant also has matches to Goff and Southworth/variants males. See the SOUTHWORTH>GOFF genetic family. These matches seem to be coincidental as they are on 61 or 67 markers, pointing to a shared lineage about 22 generations ago, around the time hereditary surnames were first adopted.
The Gough of Shropshire participant should upgrade to Big Y 700 to sort out family tree.