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.
What does Randolph mean?
From the Germanic/Old Norse name Randwulf (Rannulfr), combining 'rand' ('shield, rim') and 'wulf/ulfr' ('wolf'), meaning 'shield wolf'. Note some Norman forms became confused with Rannulf ('raven wolf').