It looks like "Gaings" to me. There are 4 people with this last name in the USA, in TN, MO, CA and TX. There are a pile of Gaings in N.Y. from 1815, also a few in NC, MO, Indiana. "Gangs" is also a possibility, and there was a Helen Gangs in Alameda CA in 1920. Could also be "Garogs", for which there is an entry (no page number showing) in "The pedigree of William Griffith, John Griffith and Griffith Grffiths (sons of Griffith, John, of the parish of Llanddewi Brefi, in the County of Cardigan...."( http://www.archive.org/stream/pedigreewilliam00glengoog/pedigreewilliam00glengoog_djvu.txt )

 (snip)IV. KYDWGAN VYCHAN, ist son of Kydwgan Vawr,  (Dwnn I, 37, &c.) called "of Carrog" or Garog, married 

 Ellen,  or Elin, who appears to have been the heiress of a great part of  the parish of Llanddeiniol, or, as it 

 was anciently called, Carrog,  or Garc^, from a small stream of that name which flows through all of his 

 remaining lands. He had issue : Thomas Griffith. Griffith Griffith,  d. s. p. David Griffith. Richard Griffith, 

 John Griffith, William Griffith,  Ahce, Gwenllian, Elen and Angharad.(end snip) (This is in the 14th century: it might just

  have given rise to a surname Garogs. Perhaps: but I can't find anyone of that surname on Google). Narings

  is also a remote possibility, and the name exists.

 Good luck