Though I can’t find an origin for Uvalda’s name, its history is inextricably linked to the railroad. The town of 530 (give or take) was incorporated in 1910 and given the name of the whistlestop on the Georgia & Florida Railway.
Railroad Street, Uvalda
Vanishing Georgia: Photographs by Brian Brown 
As for the origin of the name Uvalda, being a railroad town may offer a clue. My father, a retired trainman with the Southern Railway, used to offer comments about the names of various railway mileposts. These are locations that mark points along the tracks where junctions, signals, or water and coal were available in steam days. Aeronautical sectional charts often have very strange names where air routes intersect. My dad said the train crews named them in their typically whimsy way: after a crew member, or their mother, or the way a certain place smelled, or whatever they thought of. All of this may have nothing to do with Uvalda, but it’s a possibility. An Indian name perhaps?
The town was founded in 1909 when the railroad came through. JJ Moses gave the land that was previously a Pecan orchard to the town. The town was temporarily named “Moses” while the townspeople thought of a more permanent name. There are many stories as to how the name Uvalda came about, but the most legitimate and widely accepted one involves the railroad. A crew of men came through the town to build the railroad about 9 months after the town was founded. The foreman and the majority of his crew members were from Uvalde, TX. The prople were so excited about the railroad coming through that they decided to name the town after the place where the railroad workers were from. They changed the “e” to an “a” and the town became Uvalda, Ga.