Historical names for this district were ისანი(isani) and სოღდებილი(soɣdebili).
Etymology
Attested from the 14th century.
Origin is uncertain. Possible theories include:
Compound of ავლა(avla, “v. to go up”) +ბარი(bari, “n. valley”), therefore it would literally mean "the valley up top". Indeed, Avlabari is situated on a hill in Old Tbilisi.
Compound of ავი(avi) +ლაბიარი(labiari), literally meaning "bad neighborhood".