Literally lord (swami) of the cow (go). Honorary title for wise who have their mind unter control, they are lords of the senses.
The six disciples of Chaitanyas – Rupa Goswami, Sanatana Goswami, Raghunatha Bhatta Goswami, Jiva Goswami, Gopala Bhatta Goswami, Raghunatha Dasa Goswami – are called Goswami.