diff --git a/src/components/dialogs/limits/limits-groups-contextual-menu.tsx b/src/components/dialogs/limits/limits-groups-contextual-menu.tsx
index da0c4a94ac..dee7c961ea 100644
--- a/src/components/dialogs/limits/limits-groups-contextual-menu.tsx
+++ b/src/components/dialogs/limits/limits-groups-contextual-menu.tsx
@@ -80,28 +80,31 @@ export function LimitsGroupsContextualMenu({
     };
 
     const handleDuplicateTab = () => {
+        let newName: string = '';
         if (indexSelectedLimitSet1 !== null) {
-            const duplicatedLimits1 = getValues(
+            const duplicatedLimits1: OperationalLimitsGroup = getValues(
                 `${parentFormName}.${OPERATIONAL_LIMITS_GROUPS_1}[${indexSelectedLimitSet1}]`
             );
+            newName = duplicatedLimits1.id + '_COPY';
             const newLimitsGroup1: OperationalLimitsGroup = {
                 ...duplicatedLimits1,
-                [ID]: '',
+                [ID]: newName,
             };
             appendToLimitsGroups1(newLimitsGroup1);
         }
 
         if (indexSelectedLimitSet2 !== null) {
-            const duplicatedLimits2 = getValues(
+            const duplicatedLimits2: OperationalLimitsGroup = getValues(
                 `${parentFormName}.${OPERATIONAL_LIMITS_GROUPS_2}[${indexSelectedLimitSet2}]`
             );
+            newName = duplicatedLimits2.id + '_COPY';
             const newLimitsGroup2: OperationalLimitsGroup = {
                 ...duplicatedLimits2,
-                [ID]: '',
+                [ID]: newName,
             };
             appendToLimitsGroups2(newLimitsGroup2);
         }
-        startEditingLimitsGroup(getValues(`${parentFormName}.${OPERATIONAL_LIMITS_GROUPS_1}`).length - 1, '');
+        startEditingLimitsGroup(getValues(`${parentFormName}.${OPERATIONAL_LIMITS_GROUPS_1}`).length - 1, newName);
     };
 
     return (
diff --git a/src/components/dialogs/limits/operational-limits-groups-tabs.tsx b/src/components/dialogs/limits/operational-limits-groups-tabs.tsx
index 72ad017837..7f6f566b26 100644
--- a/src/components/dialogs/limits/operational-limits-groups-tabs.tsx
+++ b/src/components/dialogs/limits/operational-limits-groups-tabs.tsx
@@ -306,7 +306,7 @@ export function OperationalLimitsGroupsTabs({
             const newIndex: number = limitsGroups1.length;
             appendEmptyOperationalLimitsGroup(`${parentFormName}.${OPERATIONAL_LIMITS_GROUPS_1}`, '');
             appendEmptyOperationalLimitsGroup(`${parentFormName}.${OPERATIONAL_LIMITS_GROUPS_2}`, '');
-            startEditingLimitsGroup(newIndex, `LIMIT_SET`);
+            startEditingLimitsGroup(newIndex, `DEFAULT`);
         }
     }, [
         editingTabIndex,
@@ -356,10 +356,11 @@ export function OperationalLimitsGroupsTabs({
                                     {(index === hoveredRowIndex || index === activatedByMenuTabIndex) && (
                                         <IconButton
                                             size="small"
-                                            hidden
                                             onClick={(e: React.MouseEvent<HTMLButtonElement>) =>
                                                 handleOpenMenu(e, index)
                                             }
+                                            // during the naming of a limit set no other limit set manipulation is allowed :
+                                            disabled={editingTabIndex !== -1}
                                         >
                                             <MenuIcon fontSize="small" />
                                         </IconButton>
@@ -371,27 +372,31 @@ export function OperationalLimitsGroupsTabs({
                     />
                 ))}
                 <Tab
+                    key="addLimitSet"
                     label={
                         editingTabIndex === -1 && (
                             <Box
                                 sx={{
                                     display: 'flex',
+                                    alignItems: 'center',
+                                    justifyContent: 'space-between',
                                     width: '100%',
-                                    flexGrow: 1,
                                 }}
                             >
                                 <IconButton
+                                    size="small"
                                     onClick={addNewLimitSet}
                                     sx={{
                                         align: 'right',
                                         marginLeft: 'auto',
                                     }}
                                 >
-                                    <AddCircleIcon />
+                                    <AddCircleIcon fontSize="small" />
                                 </IconButton>
                             </Box>
                         )
                     }
+                    sx={limitsStyles.limitsBackground}
                 />
             </Tabs>
             <LimitsGroupsContextualMenu