Applied Math and Pure Math disaster!

I want to do Pure Mathematics for my first major, I would dual enroll for computer science but basically I am having little options for Pure Mathematics in a school I like. I was wondering if I do applied mathematics for undergrad and go to graduate for pure mathematics and then my PHD in pure consequently. Is that a thing people can do?

There are definitely people who have a PhD in pure math who did their undergrad in something else.

Yes it’s fine. The name of your degree matters less than your experience and the courses you have taken. For a strong PhD program you’ll need to have completed two semesters each of real analysis and modern algebra as an undergraduate. You’ll also want to have some exposure to complex analysis and topology.