diff --git a/jobs/templates/swh-build-docker-image.groovy.j2 b/jobs/templates/swh-build-docker-image.groovy.j2
index 22c10ce..ed1f2b4 100644
--- a/jobs/templates/swh-build-docker-image.groovy.j2
+++ b/jobs/templates/swh-build-docker-image.groovy.j2
@@ -1,63 +1,61 @@
-def organization = "softwareheritage"
 def repo_name = "{{repo_name}}"
-def image_name = "${organization}/${repo_name}"
 
 // Normalize to "latest" if we build from head commit (main or master)
 // Otherwise, keep the transmitted tag
 def tag = params.TAG
 def tag_name = ( tag == "origin/main" || tag == "origin/master" ) ? "latest" : tag
 
 // The following is configured in jenkins manually:
 // > Manage Jenkins > Configure System > Declarative pipeline (Docker)
 // Input the information in the form
 // Docker label: docker-io
 // Registry credentials: select the token created for the occasion in the docker hub
 // user (permissions required: Read / Write / Delete)
 // then click the 'Add' button
 def dockerCredentialsKeyID = 'docker-io'
 def registry_url = "registry-1.docker.io"
 
 def image_label = env.BUILD_TAG
 
 // The following pipeline uses a specific Makefile with the following targets:
 // - build: locally build the image out of the repository
-// IMAGE_NAME, TAG and IMAGE_LABEL must be provided
+// TAG, IMAGE_LABEL (to ease cleanup part) must be provided
 // - test: test the locally built image
-// IMAGE_NAME, TAG must be provided
+// TAG must be provided
 // - clean: clean up locally built image (parametric on the jenkins build)
 // IMAGE_LABEL must be provided
 // - push: publish to the registry
-// IMAGE_NAME, TAG, REGISTRY_URL must be provided
+// TAG, REGISTRY_URL must be provided
 
 node('built-in') {
   stage ('Pre-cleanup') {
     cleanWs()
   }
   stage('Checkout Repository') {
     checkout([
       $class: 'GitSCM',
       branches: [[name: tag]],
       userRemoteConfigs: [[
         url: "https://forge.softwareheritage.org/source/${repo_name}/",
       ]],
     ])
   }
   def dockerImage
   stage ('Build image') {
-    sh "make build IMAGE_NAME=${image_name} TAG=${tag} IMAGE_LABEL=${image_label}"
+    sh "make build TAG=${tag} IMAGE_LABEL=${image_label}"
   }
   stage ('Push image') {
     // first make sure the image is ok
-    sh "make test IMAGE_NAME=${image_name} TAG=${tag}"
+    sh "make test TAG=${tag}"
     // then publish it
     docker.withRegistry("https://${registry_url}", dockerCredentialsKeyID) {
-      sh "make push IMAGE_NAME=${image_name} TAG=${tag} REGISTRY_URL=${registry_url}"
+      sh "make push TAG=${tag} REGISTRY_URL=${registry_url}"
     }
     always {
       // finally clean workspace
       cleanWs()
       // and locally built image (resulting from the current jenkins build)
       sh "make clean IMAGE_LABEL=${image_label}"
     }
   }
 }