The entire experience of getting users into a new application and familiar with how to use it is referred to as "User Onboarding."
This process can include tutorials, how-to graphics & animations, or buttons & notifications pointing out new features. This is often a first-time/one-time thing, but users can usually access the content through a settings page of some kind indicated by names already suggested in prior answers.
Onboarding also includes the steps to create an account & sign-in to a service, and often continues with communications outside your app/website (email, social media, etc) to get users to come back & continue using your product. Done according to best practices, it's more than simply a "tutorial" button somewhere in the UI.
People may typically think of onboarding new users, but you can use similar techniques to introduce new features to existing users as well.
I don't think there's a specific name for any buttons, because there are many ways to accomplish this process that don't involve any buttons at all, and each case would have its unique requirements so being prescriptive may not be helpful.
Here are some resources on how you might approach user onboarding: