Let’s start off with looking at a dictionary, or even Wikipedia, for the origins of the word “Easter.” The source is clear: it comes from Eostre, an Indo-European goddess who was associated in Germanic territories with spring, and whose name was thus used to designate both the season of spring and spring festivals. In other words, the name has nothing to do with Ishtar, and the geniuses who put out that idea simply demonstrate their inability to do even the most rudimentary fact checking.
Ah, but if the holiday is named after a pagan goddess, doesn’t that make it pagan? No. First, since the name was used for spring and spring festivals, it’s not so outlandish that the important Christian feast that occurs in spring might pick up the name. More to the point, though, variants on the name Eostre are used for the holiday only in Germanic countries. In Greek, Latin, French, Italian, Russian, etc., the word for the holiday is a variant on Pascha, the name for Passover (Pesach in Hebrew). And Greek and Latin Christians were celebrating the holiday long before Christianity made it into Germanic areas. So no, it isn’t a pagan holiday whatever the etymology of the English name.
An added note: a reader pointed out this article to me that questions even the existence of the goddess Eostre. His arguments are worth considering, though I suspect Eostre was an actual goddess connected to the Titaness Eos, the goddess of the dawn in Greek mythology. Hence the reference to Indo-European mythology in my article.