Can I have a separate Apple account for my iPad or do I have to share?

You can have a separate ID, all you to do is to create a new one.

The idea of having devices with the same ID is that you can share your files and services between them.

For exemple, if you subscribe to Apple Music with your ID #1, or if you have a lot of files on iCloud Drive, the ID #2 can't directly access them. You can create a Family Sharing and add the ID #2 to the family and share things, but if they're all yours, why to have 2 IDs? Having one ID gives you access to everything you have across all your devices, I mean files, subscriptions, contacts, calendar events, etc.