Is it reasonable to call a philosopher who makes significant use of “essence” or similar terms an essentialist? I would say no. If you look at the Wikipedia article on essentialism for example, it appears to be a term of superficial classification that is used in a hostile or pejorative way. The definition given there is certainly nothing I would identify with.
I find essence to be a very useful concept. This Latin-derived term doesn’t exactly capture any single word used by Plato or Aristotle. Essence is what I call a way of being rather than a thing or property. It corresponds to the more abstract meanings of “form” and “substance”, and to what Aristotle called the “what it is” and “what it was to have been” of a thing. For both Plato and Aristotle it is an object of inquiry rather than something taken for granted. Aristotle’s notions of potentiality and actualization apply to it concepts of alternatives, development, and unanticipated change.
Aquinas’ introduction of a separate explicit concept of existence is a good example of how meanings change with context. For Aquinas, God in the act of creation gives being to possible essences. This implies that the essences are completely preformed, as Leibniz argued explicitly. Leibniz’s pre-established harmony has been viewed as deterministic, though Leibniz argued that it was not. In any case, Aquinas and Leibniz treat essences as discrete possibilities, whereas I read Aristotle as focusing on what is actualized or subject to a process of actualization. Essence as a discrete possibility is still arguably more sophisticated than what gets called “essentialism”, but it is much closer. (See also Platonic Truth; Form Revisited; Form as Value; Form, Substance.)