It’s not a supported solution, but one way to do that appears to be
https://github.com/discourse-org/postgres-bdr
edit: … except that seems to install pg9, which is odd because there is a commit in February, but that was a year ago, so maybe this isn’t a good idea. Or BDR is now supported without such heroic efforts. But I think that this isn’t the go-to place for advice on advanced Postgres configuration.
Yes, you can have multiple servers talking to the same database behind some kind of load balancer or dns pointing to both. But this isn’t the place to get advice on load balancing