We're using Route53 DNS to point to an EC2 instance: name.domain.com, and we also need access this form: domain.com/name.
What is the correct form to resolve it?
What you're asking to do is not a DNS problem, instead it's a web server problem.
Create 2 Route53
Getting your web server to recognize name.domain.com and domain.com/name as the same thing is dependent on your web server.