I'm quite not sure, if i understood the problem correctly.
You can create private hosted zone in Route 53 and configure it to a particular VPC with DNSresolution and DNS Hostname enabled.
with this, you can create an ECS instances with the above set VPC, create a service with task having a name say promotheus.local or your application (app.local) to which you want to monitor from promotheus, with this kind of set up, you can use http://app.local:port to extract monitoring information by name instead of private IP.
Ref: https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/hosted-zone-private-considerations.html
Hope this helps.
Thanks,
Sridhar