וַיִּמָּלֵ֣ט בֵּן־אֶחָ֗ד לַאֲחִימֶ֙לֶךְ֙ בֶּן־אֲחִט֔וּב וּשְׁמ֖וֹ אֶבְיָתָ֑ר וַיִּבְרַ֖ח אַחֲרֵ֥י דָוִֽד׃
И один из сыновей Ахимелеха, сына Ахитува, по имени Авиафар, убежал и убежал за Давидом.
Zohar
What is the true reason that Solomon called him (Anatot)? He wanted to tell him, during your days, my father lived in poverty, but now " go to your own fields." We should now explain why Evyatar was called Anatot. Should one assume that it was because he was from Anatot? We have already learned from the verse: "And one of the sons of Achimelech, the son of Achituv, named Evyatar, escaped" (I Sam. 22:20). And he came from Nov, the city of the priests. We have learned that Nov is also called Anatot and why is it called Anatot - because of the poverty and destitution to which it had been reduced by King Saul through the slaughter of all its priestly inhabitants. Nevertheless, Anatot was the name of a village and is not Nov. Rather, King Solomon called Evyatar Anatot, "because you were afflicted (Heb. hit'anita) in all that my father was afflicted" (I Kings 2:26) - and because he also came from the city of Nov. So the true reason is that, because King David lived in poverty in his days, he called him thus.