There are various theories about when '阿倍氏' was altered to '安倍氏,' but the most credible theory is that it happened during Enryaku era through Konin era, which was the early Heian period.
「阿倍氏」がいつ頃から「安倍氏」と改めたかには諸説あるが、平安時代初期の延暦〜弘仁年間説が有力であると言われている。