Garson \g(a)-rson, gar-son\ as a boy's name is of Old English origin, and the meaning of Garson is "son of Gar". Gar here may be a short form of Garrett, Gareth, Garland, Garrison, etc.
Baby names that sound like Garson are Carson, Karson and Gerson. Other similar baby names are Garmon, Garron, Garon, Garion, Garton, Larson and Parson.