Hm, it's rare to get questions like this here, most are on the technical side.
Usually you have one or more unique "tells" that reveal to the audience that it's one personality or the other. These personalities are usually on two ends of the behavioral extremes, e.g. good & evil, happy & glum, reserved & reckless. Then the character has one of these extremes as their "normal" everyday personalities, where the other is usually dormant.
So the "tells" can be a complete change in voice, facial expressions, physical behavior, habits specific to personalities, or even giving an accessory based on which personality is active (like a hair clip or scar appears when one is active, an obsession with ice cream, higher or lower pitched voices, an angry scowl, whatever). Depending on what kind of animation it is, it doesn't have to be realistic (like where did the hair clip come from? how'd the scar appear/disappear)?
Another kind of "tell" is the transition. If you need more reinforcement to that notion, then make it obvious when the character changes personality. Flashes of light, spasms, or if something triggers it then make it fairly obvious what it is.
And usually a character with split personalities has some interaction between the two, where at least one is aware of the other and his/her actions. Seeing and engaging with the other in a reflection, or talking to himself/herself out loud, or having a ghost or mini-version riding on his/her shoulder nagging at the other personality all helps get the point across.
