diff --git a/compose.coolify.esignet.yaml b/compose.coolify.esignet.yaml
index e4b0c52..d2eb6ec 100644
--- a/compose.coolify.esignet.yaml
+++ b/compose.coolify.esignet.yaml
@@ -87,7 +87,7 @@ services:
     labels:
       solmara.rollout.slot: authority-cells
 
-  esignet-ui:
+  esignet_ui:
     image: ${SOLMARA_ESIGNET_UI_IMAGE:?set digest-pinned eSignet UI image}
     environment:
       SOLMARA_ESIGNET_PUBLIC_HOST: ${SOLMARA_ESIGNET_PUBLIC_HOST:-esignet.solmara.registrystack.org}
@@ -102,7 +102,9 @@ services:
   # neither its OpenID discovery document nor its RFC 8414 authorization-server
   # metadata. The UI image is a host-agnostic reverse proxy that serves both at
   # the root and forwards /v1/esignet, so it also fronts the issuer origin.
-  esignet-edge:
+  # Coolify matches a routed service against the compose key but resolves it
+  # after rewriting "-" to "_", so both proxies carry underscore names.
+  esignet_edge:
     image: ${SOLMARA_ESIGNET_UI_IMAGE:?set digest-pinned eSignet UI image}
     environment:
       SOLMARA_ESIGNET_PUBLIC_HOST: ${SOLMARA_ESIGNET_PUBLIC_HOST:-esignet.solmara.registrystack.org}
diff --git a/scripts/test_hosted_esignet_topology.py b/scripts/test_hosted_esignet_topology.py
index d70fc87..4a7e1d1 100644
--- a/scripts/test_hosted_esignet_topology.py
+++ b/scripts/test_hosted_esignet_topology.py
@@ -46,15 +46,15 @@ def test_compose_is_a_standalone_esignet_app(self) -> None:
                 "esignet-database",
                 "esignet-redis",
                 "esignet",
-                "esignet-ui",
-                "esignet-edge",
+                "esignet_ui",
+                "esignet_edge",
                 "esignet-seed",
             },
         )
         # The issuer origin is fronted by the proxy image, not by eSignet
         # itself, so its discovery documents are reachable where the issuer
         # says they are.
-        self.assertEqual(services["esignet-edge"]["image"], services["esignet-ui"]["image"])
+        self.assertEqual(services["esignet_edge"]["image"], services["esignet_ui"]["image"])
         self.assertNotIn("solmara.lab.host", services["esignet"]["labels"])
         self.assertNotIn("portal", services)
         self.assertEqual(
diff --git a/scripts/test_runtime_topology.py b/scripts/test_runtime_topology.py
index 8a2b692..791a3dd 100644
--- a/scripts/test_runtime_topology.py
+++ b/scripts/test_runtime_topology.py
@@ -751,8 +751,8 @@ def test_hosted_esignet_is_standalone_and_core_portal_owns_login_config(
                 "esignet-database",
                 "esignet-redis",
                 "esignet",
-                "esignet-ui",
-                "esignet-edge",
+                "esignet_ui",
+                "esignet_edge",
                 "esignet-seed",
             },
         )
@@ -813,16 +813,28 @@ def test_hosted_esignet_publishes_discovery_at_its_issuer_root(self) -> None:
         straight at it leaves `{issuer}/.well-known/openid-configuration` and the
         RFC 8414 authorization-server document unserved. The UI image is a
         host-agnostic reverse proxy that publishes both, so the public host
-        belongs to an edge instance of it and the service stays unrouted."""
+        belongs to an edge instance of it and the service stays unrouted.
+
+        Both proxies carry underscore names because Coolify accepts a routed
+        service only under its compose key but resolves it after rewriting "-"
+        to "_", so a hyphenated name is stored where routing never reads."""
         esignet_path = SCRIPT.parents[1] / "compose.coolify.esignet.yaml"
         services = yaml.safe_load(esignet_path.read_text(encoding="utf-8"))["services"]
-        edge = services["esignet-edge"]
-        self.assertEqual(edge["image"], services["esignet-ui"]["image"])
+        edge = services["esignet_edge"]
+        self.assertEqual(edge["image"], services["esignet_ui"]["image"])
         self.assertEqual(
             edge["labels"]["solmara.lab.host"],
             "${SOLMARA_ESIGNET_PUBLIC_HOST:-esignet.solmara.registrystack.org}",
         )
         self.assertNotIn("solmara.lab.host", services["esignet"].get("labels") or {})
+        routed = [
+            name
+            for name, service in services.items()
+            if "solmara.lab.host" in (service.get("labels") or {})
+        ]
+        self.assertEqual(sorted(routed), ["esignet_edge", "esignet_ui"])
+        for name in routed:
+            self.assertNotIn("-", name)
 
     def test_bruno_workspace_covers_only_the_eight_governed_v2_lookups(self) -> None:
         relay_requests = SCRIPT.parents[1] / "requests/registry-lab/50 - Relay V2"