Fix cloud deploy PR job after removing cloud image (#115857)

* Fix cloud deploy PR job after removing cloud image
* Fix task name for building cloud ess docker image in cloud deploy

Author: breskeby

.buildkite/scripts/cloud-deploy.sh

@@ -2,11 +2,11 @@
 
 set -euo pipefail
 
-.ci/scripts/run-gradle.sh buildCloudDockerImage
+.ci/scripts/run-gradle.sh buildCloudEssDockerImage
 
 ES_VERSION=$(grep 'elasticsearch' build-tools-internal/version.properties | awk '{print $3}')
-DOCKER_TAG="docker.elastic.co/elasticsearch-ci/elasticsearch-cloud:${ES_VERSION}-${BUILDKITE_COMMIT:0:7}"
-docker tag elasticsearch-cloud:test "$DOCKER_TAG"
+DOCKER_TAG="docker.elastic.co/elasticsearch-ci/elasticsearch-cloud-ess:${ES_VERSION}-${BUILDKITE_COMMIT:0:7}"
+docker tag elasticsearch-cloud-ess:test "$DOCKER_TAG"
 
 echo "$DOCKER_REGISTRY_PASSWORD" | docker login -u "$DOCKER_REGISTRY_USERNAME" --password-stdin docker.elastic.co
 unset DOCKER_REGISTRY_USERNAME DOCKER_REGISTRY_PASSWORD