The relative pronoun who(m) refers to animate beings, like people or animals. Personalities, in the meaning it has in your example, means the characteristic traits of a person. A person's personality is not an animate being. You can't take it to the beach, for example, or feed it donuts. The personality of a person is an inanimate object (a thing). The relative pronoun which is used to represent inanimate things.
A defining relative clause gives us extra information which helps the listener to understand which things we are talking about:
- The man who you saw yesterday is my best friend.
Here, who you saw yesterday tells us exactly which man we are talking about. A non-defining relative clause, on the other hand, gives us extra information about something or somebody we can already identify:
- Your father, whom I've known for twenty years, is the most honest man
I've ever met.
Here, the relative clause whom I've known for twenty years, is just giving the listener extra information. It is not helping the listener understand which of her fathers we are talking about!
The relative item that can be used for both things and people/animate beings. However it can only be used in defining relative clauses, and not non-defining ones:
- Your father, that I've known for twenty years, is the most honest man
I've ever met* [wrong]
- The man that you saw yesterday is my best friend. [correct]
- The sandwich that you bought looked very tasty. [correct]
That cannot occur after a preposition that has been moved to the front of the relative clause:
The options for your examples then are:
A Jekyll and Hyde is a person who has two pesonalities, one of which is bad and the other good.
He invents a drug which/that can separate them. When he takes the drug, he becomes an evil version of himself, who(m) he calls Mr. Hyde.