Android Bottom Navigation View Customisation
Use the SpaceNavigationView library to get the Bottom Navigation Bar similar to your required design. The library has the option for an overflow icon in the center and also there is no title with icons. However, I am not sure if the is any background color change feature on selection of tab in the library. You can also take a look at other libraries and see if the source codes can be of any help.
https://github.com/armcha/Space-Navigation-View
https://github.com/aurelhubert/ahbottomnavigation
https://github.com/sephiroth74/Material-BottomNavigation
https://github.com/Ashok-Varma/BottomNavigation