
Would this be used to ask someone to summon a doctor or to remind someone to please use the correct title of doctor when addressing the speaker?

It would only be used for the former.
However, there is this well-known joke.
"Please call me a taxi."
"OK. You're a taxi."

To say you want to be addessed with that title:
"Please call me 'Doctor'"
Or: "Please address me as 'Doctor'"

Thanks. If the other sentences and the joke are not yet on Tatoeba, maybe you would like to add them?

https://tatoeba.org/eng/sentences/show/424924
"Please call me a taxi."
"OK. You're a taxi."
Paul Blay added it.
This is also in the database as a single non-joke sentence.
[#6009218] Call me a taxi. (mailohilohi) *audio*
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