It is called “Customization”. Customization is done to create “Personalization”.
“Personalization” is dynamically tailoring an application or website according to the user. It's more of a strategy which itself is a UX plan. Personalization can be active and passive.
“Active Personalization” is something which is provided by the options, a user defined.
Example: You went on Amazon and searched for Apple Phones and Virtual Reality Headsets. Next time you log in, there will be list of iPhone & VR headsets shown on the page.
In your example, after selecting genre/artist of you interest, you’ll be shown those on a major basis with some recommendations of another genre/artist in a separate list or in between. Though it depends on the specific organization strategy.
“Passive Personalization” is something which is machine based which is done by tracking the user behavior which is also called “Behavior Targeting”.
Example is geo-location. System automatically gives us results based on this.
To start with this, we do user research, we collect data, data on what user needs/likes/dislikes and put those options on the app or website for user to select which we call filters or questionnaire. The entire process where a user logs in, selects, okays and perform the action is “User Flow”.
The filters/questionnaires we give are called "Filtering" which can be further divided into “Collaborative, Content-Based and Hybrid” by which we can make sure, what a user wants/likes/dislikes and then show them the results as per their previous selections.
You can see this examples in Facebook, LinkedIn, Netflix, Amazon, Google, News Articles etc.
Hope this helps a bit.