What does Rudolph mean?
From the Germanic name Hrodwulf, combining 'hrod' ('fame') and 'wulf' ('wolf'), hence 'famous wolf'. The '-olph/-olf' ending preserves the wolf element.
What does Reginald mean?
From Germanic 'ragin' ('counsel, advice') + 'wald' ('rule, power'), i.e. 'ruler by counsel' / 'counsel-power'. Note: this is 'ruler/power', NOT literally 'king'. Reynold and Ronald are closely related forms.