The Share UI is one of few things that haven't changed since Windows 8, but if you hate it as much as many people do, you're in luck, as Microsoft will be redesigning it for the upcoming Creators Update.
Here's what it looks like in current builds of Windows 10, as well as in Windows 8:
Here's a look at what the UI currently looks like in the most recent Insider Preview build, 14971. You'll notice that instead of showing the names of apps, it shows package names:
As you can see, it still needs some work, which is why it's not enabled in the build by default. You can set it up manually though by making some changes to the Registry.
Be warned though that Registry edits are not to be taken lightly. A wrong step can put your PC in a rough spot and you might have trouble fixing it. If you really want to check out the new UI for yourself, you can follow these steps (via MSPU):
Open Run (Win + R)
Type in “regedit” and hit enter to open the registry editor
In the address bar on the registry editor, simply copy and paste this: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\SharePlatform and hit enter
After that, right click to open up the context menu and then create a new “DWORD (32-bit) value” with the name “EnableNewShareFlow”
Double-click the newly created DWORD value, and change the value to 1