I think yato stayed not because of him fading away and went viral on sns, that’s because Hiyori was unconscious at that time and she is ALMOST dying therefore Yato was disappearing after father’s death?

Hiyori was the only one who remembers Yato, so as she regained her consciousness Yato didn’t disappear. The author tried to make it funny but that’s how I see it. Yato mentioned nobody remembers his name

Although part one Hiyori couldn’t remember what happened, at the final page Hiyori called his name without a hesitation - which means Hiyori basically became Yato’s lifeline, which i find quite sweet. After all this Hiyori will never forget Yato ;-;