diff --git a/runtime/starpu/codelets/codelet_map.c b/runtime/starpu/codelets/codelet_map.c
index 97de57e26efa988a6e425573d637d13115f8f2d3..15512bf6bdf0e345ab81be7ebd42999e5c2759a9 100644
--- a/runtime/starpu/codelets/codelet_map.c
+++ b/runtime/starpu/codelets/codelet_map.c
@@ -9,10 +9,10 @@
  *
  * @brief Chameleon map StarPU codelet
  *
- * @version 1.2.0
+ * @version 1.3.0
  * @author Mathieu Faverge
  * @author Florent Pruvost
- * @date 2022-02-22
+ * @date 2023-07-06
  *
  */
 #include "chameleon_starpu.h"
@@ -49,11 +49,15 @@ void INSERT_TASK_map( const RUNTIME_option_t *options,
 
     struct starpu_codelet *codelet = &cl_map;
     void (*callback)(void*) = options->profiling ? cl_map_callback : NULL;
+    char                  *cl_name = "map";
 
     CHAMELEON_BEGIN_ACCESS_DECLARATION;
     CHAMELEON_ACCESS_RW(A, Am, An);
     CHAMELEON_END_ACCESS_DECLARATION;
 
+    cl_name = chameleon_codelet_name( cl_name, 1,
+                                      A->get_blktile( A, Am, An ) );
+
     rt_starpu_insert_task(
         codelet,
         STARPU_VALUE,    &A,                      sizeof(CHAM_desc_t*),
@@ -67,7 +71,7 @@ void INSERT_TASK_map( const RUNTIME_option_t *options,
         STARPU_CALLBACK,  callback,
         STARPU_EXECUTE_ON_WORKER, options->workerid,
 #if defined(CHAMELEON_CODELETS_HAVE_NAME)
-        STARPU_NAME, "map",
+        STARPU_NAME, cl_name,
 #endif
         0);
 }