The sentence:
'Doctor' means 'a learned man', which I suppose this man is.
is perfectly grammatical, because the antecedent of "which" is "the condition of being a learned man", which -- being a condition -- is not a specific person. The indefinite article makes the noun phrase sound like a quality, as if it were adjectival (the quality of a person) rather than nominal (the name of a person).
Another example:
- I called him a liar, which he is.
There is also a grammatical reason why "which" and not "who" or "whom" is correct, and that is the function of the antecedent in the relative clause -- a subject complement:
I suppose this man is a learned man.
He is a liar.
Instead, if the function in the antecedent is "more nominal", so to speak (for example subject or object), then "who" will be used:
- He is so aggressive people call him Hitler, who I think was much more cruel than he is. (Hitler was much more cruel.)