Georgians refer to themselves as ქართველი (qartveli) and their country as საქართველო (saqartvelo).  So where does the name “Georgia" come from?  Though there are many theories on this matter, two stand out as the most plausible:

1) The local popularity of St. George—the dragon slayer—led to the proliferation of cults devoted to St. George and the spread of the name “George” and association between St. George and the Georgians.  

2) The name “Georgia” is semantically linked to Greek roots: γεωργία (transliterated “georgía”), and γεωργικών (transliterated “georgikós”), meaning “agriculture” and “agricultural” and probably reflecting the local agricultural and vinocultural prowess.  As the Greek presence gave way to various Persian empires from 536 B.C.E. to 638 C.E., Georgians were called “Gurjhan” (Gurzhan/Gurjan), or “People from گرجستان (Gurj).” The early Islamic/Arabic sources spelled the name Kurz/Gurz and the country “جورجيا” (Gurjistan)—reflected in the modern Turkish “Gürcistan”. Any or all of these linguistic sources could have easily evolved into or contributed to the modern name “Georgia”.