Current:
$x_{1}$ is a person/people (noun) [not necessarily human]; $x_{1}$ displays personality/a persona.
Suggest:
$x_{1}$ is a person [not necessarily human], displaying personality $x_2$ (ka, plural).
The x2 refers to any properties satisfied by x1 that describe sentient behaviors that back up x1's personhood and optionally distinguish x1 from other similar persons.
That is, your personality consists meaningfully of (λx. x is prone to anger), and trivially also (λx. x can feel pain), but not (λx. x weighs 60 kg) or (λx. x needs food to survive).
Current:
Suggest:
The x2 refers to any properties satisfied by x1 that describe sentient behaviors that back up x1's personhood and optionally distinguish x1 from other similar persons.
That is, your personality consists meaningfully of (λx. x is prone to anger), and trivially also (λx. x can feel pain), but not (λx. x weighs 60 kg) or (λx. x needs food to survive).