Beech, Birch, and even Maple are what we call a diffuse-porous wood species (also known as a closed grain wood). With contact/use the grains on a diffuse-porous wood species will continue to condense and harden making the bat more dense and the wood harder and less susceptible to breaks. Just as Birch hardens on use,
European Beech will continue to get hotter as you use it.
As you use the bat you'll begin seeing the grains/striations of the beech wood. This is common and exactly what you want to see out of your bat. Seeing the grains are a good indication that the grains in your bat are beginning to compress. As the wood grains compress, the bat takes on a higher density - and all things being equal, a ball will travel further when hit with a denser bat. Any dents you may be seeing are likely just dents in the paint finish that is on the bat and not necessarily on the wood itself.
Ash, on the other hand, is a ring-porous wood species and will actually lose density and flake with extended
use.