Does business name need to be in title tag?

Does the business name have to be in your title tag?

What if the domain already had the business name in it?

It depends on the "brandability" of your business... but 99% of the times is very important, therefore it should go in the title as very good practice (people can easily recognize where info is coming from, and Google loves brands for some weird reason I've found through this year)

From my point of view, domain name is barely useless in terms of anything related SEO. I got extremely stucked in this topic time ago, and now I have it seriously ditch it. In fact, it has been proven that despite domain is not even a minor ranking factor nowadays, the slug is somewhat key

So in conclusion: Use your brand as much as you can. And if it's a local business, use your brand twice for local SEO purposes.

Exactly what has been said above. I simply like to use the brand as the domain due to people recognizing it.

You should use it at the end of the title

Yeah, you should use it. It's a standard practice. Check the title of this page and you'll see it has the brand name after the thread title, it's like this for pretty much any other site.