It is always best to use your Laptop's Manufacturer's drivers. You can alway use AMD Generic drivers if they are much newer and needed to run newer games or applications. But they may not take full advantage of your Laptop's features.
AMD Laptop drivers may change the GPUs name but it will be the same as the one installed on the laptop. Using the Laptop's manufacturer driver will correctly show the proper name for your GPUs in your laptop.
This is AMD Forum's procedure to update your Laptop using AMD drivers : Laptop graphics update...How to and this is how to configure your Laptop to be switchable : Configuring Laptop Switchable Graphics on a Windows® Based System .
This is a bit outdated but it show how to configure a HP Laptop from HP Support: HP Notebook PCs - Switchable Graphics on Notebooks Configured with Intel and ATI GPUs | HP® Customer Support
This WIndowsTen thread may be useful: Windows 10 Help Forums