'Barliman' comes from 'Barley-man', meaning a brewer or innkeeper 'Butterbur' is the name of a plant, one of the typically botanical names used by the Men of Bree
Barliman's dates of birth and death are not recorded, but he's often referred to in The Lord of the Rings as 'old Barliman' or 'old Butterbur'. On that basis, it's probably fair to assume he was born no later than about III 2968 (that is, he would be fifty or more years old when he first encountered Frodo Baggins - who would have been around the same age - in III 3018).