This enzyme belongs to the family of ligases, specifically those forming carbon-nitrogen bonds as acid-D-amino-acid ligases (peptide synthases). The systematic name of this enzyme class is gamma-L-glutamyl-L-cysteine:beta-alanine ligase (ADP-forming). Other names in common use include homoglutathione synthetase, and beta-alanine specific hGSH synthetase.
References
Macnicol PK (1987). "Homoglutathione and glutathione synthetases of legume seedlings - partial-purification and substrate-specificity". Plant Sci. 53 (3): 229–235. doi:10.1016/0168-9452(87)90159-2.