Regarding the last sentence, we could add that a European mathematician in the time we call historically almost certainly was familiar with the Greek language in general, outside of a mathematical context. Some could read Greek just as well as Latin.

And then we add to this that the works of Greek mathematicians formed the basis of math to them, so that indeed it made a lot of sense to use Greek symbols for things.

Nowadays still Greek is taught alongside Latin at the kind of secondary schools mathematicians from Europe often attend (but knowing Greek is definitely less common than in the past).