Show Posts of a Category inside a Page

In my blog I have some Categories and some Pages. In some of this pages I need to show the content of the category with the same name of this page but if don’t have a category with the same name, then just the page itself is show.

There’s a plugin named Category Page that did this in the past, but now it’s not updated.

So here is the thing:

Ex1. I have one Page named Design and a category named Design as well, so when someone enter in the Design Page it will show the Page Content and the category content in the bottom.

Ex2. I have one Page named Contact, but don’t have a category named that, so when someone enter on the Contact Page, it will show just the content of the page.