Middle English bihoven, from Old English behofian "to have need of, have use for," verbal form of the ancient compound word represented by behoof (q.v.). From c. 1200 as "be fit or meet for, be necessary for," now used only in the third person, with it as subject. Related: Behooved; behooving.
Historically, it rimes with move, prove, but being now mainly a literary word, it is generally made to rime with rove, grove, by those who know it only in books. [OED]
<a href="https://www.etymonline.com/word/behove">Etymology of behove by etymonline</a>
Harper, D. (n.d.). Etymology of behove. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/behove