diff --git a/test/e2e/storage/external/external.go b/test/e2e/storage/external/external.go
index <HASH>..<HASH> 100644
--- a/test/e2e/storage/external/external.go
+++ b/test/e2e/storage/external/external.go
@@ -253,7 +253,7 @@ func (d *driverDefinition) GetSnapshotClass(config *testsuites.PerTestConfig) *u
 		framework.Skipf("Driver %q does not support snapshotting - skipping", d.DriverInfo.Name)
 	}
 
-	snapshotter := config.GetUniqueDriverName()
+	snapshotter := d.DriverInfo.Name
 	parameters := map[string]string{}
 	ns := config.Framework.Namespace.Name
 	suffix := snapshotter + "-vsc"
e2e/storage: fix snapshot support in external driver testing

When using an already installed driver, the snapshot name is the
original driver name. Renaming was incorrectly copied from the in-tree
CSI hostpath driver.