Learn Italian: Il dottore medesimo ha chiamato.

When medesimo (or stesso) is placed after the noun, it adds emphasis, meaning "himself", "herself", or "itself" (as in, "The doctor himself"). If it were placed before the noun (il medesimo dottore), the meaning would change to "the same doctor".

Could I use stesso instead of medesimo in this sentence?

Yes, absolutely. Il dottore stesso means exactly the same thing. Medesimo is simply a slightly more formal or elevated synonym for stesso, but they follow the exact same grammatical rules and are highly interchangeable.

Does medesimo change its ending depending on who called?

Yes. Even though it translates to an English pronoun here, medesimo functions as an adjective in Italian and must agree in gender and number with the noun it emphasizes. If a female doctor called, the sentence would be La dottoressa medesima ha chiamato.

Does using medesimo make the verb reflexive?

No, medesimo simply emphasizes the subject. The verb ha chiamato is just the active past tense meaning "he called" (for example, on the phone). If you wanted a true reflexive meaning like "he called himself", you would need the reflexive pronoun si, not an adjective.