Because each pod has a dynamic IP address and, usually, a dynamic name (for example, if you use Deployment), you don't have a chance to make its' endpoint static somehow, but you have an alternative way - StatefulSet with Headless Service.

You can deploy several replicas of your application using StatefulSet and create Headless Service for it. Each replica in the StatefulSet will be available using its unique name.

Here's the quote from the documentation:

Each Pod in a StatefulSet derives its hostname from the name of the StatefulSet and the ordinal of the Pod. The pattern for the constructed hostname is $(statefulset name)-$(ordinal). The example above will create three Pods named web-0,web-1,web-2. A StatefulSet can use a Headless Service to control the domain of its Pods. The domain managed by this Service takes the form: $(service name).$(namespace).svc.cluster.local, where “cluster.local” is the cluster domain. As each Pod is created, it gets a matching DNS subdomain, taking the form: $(podname).$(governing service domain), where the governing service is defined by the serviceName field on the StatefulSet.