Sheild Initials

[George M. Purtill Member #28]

I failed to watch enough Martha Stewart shows before she went to prison so forgive me if I dont know the proper conventions on monagrams.
I have a DHE Double trap gun (also shoots turkeys well) and I am working on the provenance.
It once belonged to an avid trapshooter in Connecticut I am told.
the letters appear to be "HHG".
However as i have learned from family hand me down linens, sometimes what appears to be the middle initial is actually the last initial?
I would like to look for this trapshooter in CT circa 1928 but want to know if I should be looking for HHG or HGH???
This picture is not real good (iPhone) but its really the style of engraving that's inportant: the letters bend at the curves of the shield.