How do I set up DNS on cPanel?

The reason you're seeing the "members" portion in the nameserver record is because cPanel thinks that lixxxx-xxx.members.linode.com is your domain name by default during setup. As you pointed out, this is wrong, as they don't actually exist as nameservers. You have two options from here:

1) Use a "vanity" name sever domain like ns1.example.com that is managed locally on your server.
2) Use an external DNS service (like Linode’s DNS Manager) and configure the associated name servers (like ns1.linode.com).

In order for the first option to work, you'll need to actually register your nameservers with your registrar first. You'll then want to make sure your A records have been added to your Linode through WHM. cPanel should automatically configure your DNS records once you add your domain.

For option number two, you would need to add your domain to our DNS Manager. From here, you'll need to manually add/remove/update DNS records as necessary.

We have a guide on how to get started with this here:

Set Up DNS Services on cPanel

Additionally, cPanel has a step-by-step guide on setting up nameservers:

How to Set Up Nameservers in a cPanel Environment

There is no wrong answer here, and whichever route you take will depend on your needs moving forward. Hopefully this gives you a couple places to start from!