Or HaChaim on Exodus 4:5/אור החיים על שמות ד׳:ה׳

1 למען יאמינו כי נראה אליך השם. "So that they will believe that G'd has appeared to you." The reason that G'd kept repeating "the G'd of their fathers," may have been to hint to the people present that unless one believed in the G'd who had been the G'd of the patriarchs one could not hope to achieve control over the serpent, i.e. the forces of evil in this universe. A demonstration of such control would therefore imply that one was on intimate terms with G'd.