Catalysis of the reaction: UDP-N-acetyl-D-galactosamine + alpha-D-galactosyl-(1->4)-beta-D-galactosyl-(1->4)-beta-D-glucosylceramide = UDP + beta-N-acetyl-D-galactosaminyl-(1->3)-alpha-D-galactosyl-(1->4)-beta-D-galactosyl-(1->4)-beta-D-glucosylceramide.
UDP-N-acetylgalactosamine:globotriaosylceramide beta1,3-N-acetylgalactosaminyltransferase activity