internal name (name to be used in URL to download the asset) is not correct in browser UI and "Edit Asset" UI.
This especially causes confusion when author duplicates a file and moves it to another folder. oldfolder/image.jpg newfolder/image0.jpg but in UI it isshown as image.jpg which causes confusion.
Magnolia Version: 5.3.5, 5.4.4

EDIT
The node name could be changed to something like foo0.png rather than foo.png0 and the asset name likewise, else one cannot distinguish at a first glance what's the copy and what's the original (unless one looks at the node name). After duplication one could end up with something like this

AGREEMENTS

After fixing the bug, there are some OK cases that you will found regarding to asset name.
1. In case asset name has extension

2. In case asset name has not extension

3. In case asset name does not have the same base name with node name. This case happened when we tried to rename asset by Rename node action. This case still ok due to this ticket just supported to make the filename reflect real node name