Why is the Markowitz model called mean-variance?

Question

Because it actually minimizes the variance... shouldn't it be minimum-variance model? :)

Answer 1

The model is called mean-variance, because it studies the relationship between return (as represented by mean return over a long period of time) and risk (as represented by variance of returns).

Answer 2

No it links mean (return) and Variance. You can find the minimum variance portfolio if you want, but that s not the only interesting result you can find in Markowitz model.
In fact, you will use the point where the capital market line touch the efficient frontier (markowitz) and not the minimal variance portfolio