Maybe mask around the area you want the Georgi label to be, paint it white with fabric paint to cover the existing logo and then hand paint on the Georgi label? You could also make the Geogi label out of paper and just cover the existing label, though crinkling paper could become irritating after a while.
Or, you could use a white square of fabric as a label, lay it out on the floor, paint it with fabric paint to look like the Georgi Vodka label, and after it's dried just glue or hand sew it to the costume, I'd go with fabric glue myself.
Another way to go that would look great, is to scan the label off of a Georgi bottle at a REALLY high resolution. take that file to a place like Kinkos, and have them resize it and print out a poster size print of it on that white plastic material they have. Then glue that over the label on the costume.
That's pretty much what this guy did to make this Jagermeister costume: