From 御(お) (o-) + 忍(しの)び (shinobi, “連(れん)用(よう)形(けい) (ren'yōkei, “stem or continuative form”) of the verb 忍(しの)ぶ (shinobu).”).
おしのび • (o-shinobi) ←おしのび (osinobi)?