It's a bid odd to name a revolver, don't you think? The revolver is there, always beckoning, always offering an alternative: death, which is an idea that Willie played with prior to the beginning of the play:
Remember how you used to keep on at me to take it away from you? Take it away, Winnie, take it away, before I put myself out of my misery. (1.29)
Depending on how you interpret the ending, it could be said that he is still contemplating this idea through the end of the play
Also, since it's been given a name and always seems to float to the top of Winnie's bag, we could assume that the revolver actually has a mind of its own and that it is actively presenting itself as a way out for Winnie and Willie. Or maybe it was Beckett's way of presenting his characters with a challenge—a way of tempting them to take the easy way out.
The Revolver also functions as a phallic object, one that Winnie controls. What does that say about power, specifically as it relates to the balance of power in Winnie and Willie's relationship?
In a way, Winnie has the power over life and death. She could easily end their misery, but she doesn't. And yet, Winnie always keeps the revolver close at hand. Does the revolver offer her comfort? If so, why does she need the constant reminder that there is another way out of the world of the living?