In De Interpretatione 1a1, Aristotle defines and describes homonymy in the following way:
When things have only a name in common and the definition of being which corresponds to the name is different, they are called homonymous. [E.g.,] both a man and a picture are animals. These have only a name in common and the definition of being which corresponds to the name is different; for if one is to say what being an animal is for each of them, one will give two distinct definitions.
Let's apply this to Kenny's example. One thing a doctor, a scalpel, and a cancer have in common is the name 'medical': a doctor is a medical person, a scalpel a medical instrument, and a cancer a medical problem. The question is whether the 'definition of being' which corresponds to 'medical' is the same for all three. To answer, let's ask: what does it mean for each of those things to be medical?:
- A doctor is medical in the sense that she is a professional who practices medicine.
- A scalpel is medical in the sense that it is ordinarily used during medical operations.
- A cancer is medical in the sense that it is a condition that requires medical attention.
For those things, a different definition of what makes the thing medical is used, so they're said to be homonymous. Contrast that with an example Aristotle gives of synonymous things (1a6):
- A man is an animal in the sense that [insert: your definition of what makes something an animal].
- An ox is an animal in the sense that [insert: your definition of what makes something an animal].
For these things, the same definition of what makes the thing an animal is used, so they're said to be synonymous. These definitions have certain arbitrariness to them, but the bigger problem here is that:
- Aristotle assumes that there is such a definition of being;
- Aristotle assumes that that definition of being is unique.
I have tried to guess how Aristotle might have justified the claim that medical man, medical instrument, and medical problem are homonymous. But the explanation I've given rests on Aristotle's assumption that "the definition of being" denotes a unique object, an assumption that you and I might not share. For example, we might, as the OP has, propose a definition of 'medical' in such a broad way that it can act as a definition of being medical for all three things; and so on. There are lots of other avenues open.
Ackrill, J.L. (1963) Aristotle's Categories and De Interpretatione, Clarendon, Oxford.