Where does “Haru” come from?

Haru (Atayal) comes from Japanese はる, from Old Japanese 春 — the spring.

Ancestry of “Haru”, step by step

Step	Language	Word	Meaning
1	Japanese	はる	verbal suffix expressing respect to subject of verb; X-a-haru is equivalent to standard o-X-i ni naru
2	Old Japanese	春	the spring