Take the suffix of internal names from the Input and never the environment: Input.InternalSuffix and a local internal-name helper, so the package doc is true (review round 1, finding 5). The test failed first; the suite is 1257 tests in 1.04 s

go/compose/network.go

@@ -37,6 +37,19 @@ func (c *composer) say(format string, args ...any) {
 	c.said = append(c.said, line)
 }
 
+// suffix is what the mesh's internal names end in: the Input's, and overlay.DefaultSuffix when it gives none. The package never calls
+// overlay.Suffix or overlay.InternalName, which read the environment, so the assigner and the controller compose the same names
+// from the same Input.
+func (c *composer) suffix() string {
+	if v := strings.TrimPrefix(strings.TrimSpace(c.in.InternalSuffix), "."); v != "" {
+		return v
+	}
+	return overlay.DefaultSuffix
+}
+
+// internalName is a node's name inside the mesh.
+func (c *composer) internalName(node string) string { return node + "." + c.suffix() }
+
 // overlayRange is the range the mesh allocates node addresses from: the adopted tunnel's first (novox/hq ADR 0105),
 // then the range genesis was told, then the default.
 func (c *composer) overlayRange() string {
@@ -203,7 +216,7 @@ func (c *composer) whereEveryoneIs() (map[string]string, error) {
 	}
 	out := map[string]string{}
 	for _, p := range c.onTheNetwork() {
-		out[p.Name] = overlay.InternalName(p.Name)
+		out[p.Name] = c.internalName(p.Name)
 	}
 	return out, nil
 }