How to verify real people?

How much code do you want to write?

One possible way to do this is to have the musician log in to your site with the Facebook account that controls their Facebook page. You can then automatically check with the Facebook API to see if that account actually does have admin access to the band's Facebook page, and then you have instant, hassle-free verification.

Are you afraid from bots and spam? Or from people who pretend to be real bands, but are actually garage amateurs?

I believe it's the latter - Therefore a requirement of a website/social media page for a manual check seems the best way for me. Bands usually put their songs/images/performances.

You can also require a band to have 3 publicly accessible songs (on their own "official" YouTube or other site) before qualifying for being a user.

Does it make sense?

Airbnb solved this issue by using both online and offline indicators.

https://www.airbnb.com/help/article/450

However, for your product, this seems a bit excessive but will solve the identity issue.

Online

You can require people to link to their social media accounts such as Facebook & Twitter. This would even open up possibilities in the future to allow your site to scrap info from their feeds or say auto-post tweets/posts.

Offline

This is not really offline - but uses offline information. There are a couple of approaches. You can require a government ID or ask a series of questions based on publicly known information.

Recommendation

I am not sure what risk you are trying to mitigate. If someone misrepresents their identity, then they are committing fraud and your terms of service can address this.

I would just build in the ability to verify an account with a link to a social media site like facebook or twitter. Require that these social accounts be active (say 3 posts in last 30 days). This would provide some assurance.

You can then publish a dispute process that allows any legitimate band to notify you of potential fraud.

This provides reasonable and automated identify verification without spending tons of effort in fixing a problem that you don't actually have (yet).