diff --git a/src/fastmcp/server/server.py b/src/fastmcp/server/server.py
index c758f64cb..9d75ea037 100644
--- a/src/fastmcp/server/server.py
+++ b/src/fastmcp/server/server.py
@@ -464,7 +464,12 @@ class FastMCP(Generic[LifespanResultT]):
                 child_tools = await mounted.server.get_tools()
                 for key, tool in child_tools.items():
                     new_key = f"{mounted.prefix}_{key}" if mounted.prefix else key
-                    all_tools[new_key] = tool.model_copy(key=new_key)
+                    all_tools[new_key] = tool.model_copy(
+                        key=new_key,
+                        update={"name": f"{mounted.prefix}_{tool.name}"}
+                        if mounted.prefix
+                        else {},
+                    )
             except Exception as e:
                 logger.warning(
                     f"Failed to get tools from mounted server {mounted.server.name!r}: {e}"
@@ -722,7 +727,9 @@ class FastMCP(Generic[LifespanResultT]):
                     key = tool.key
                     if mounted.prefix:
                         key = f"{mounted.prefix}_{tool.key}"
-                        tool = tool.model_copy(key=key)
+                        tool = tool.model_copy(
+                            key=key, update={"name": f"{mounted.prefix}_{tool.name}"}
+                        )
                     # Later mounted servers override earlier ones
                     all_tools[key] = tool
             except Exception as e:
diff --git a/tests/server/test_mount.py b/tests/server/test_mount.py
index d02e86b6c..bfb8d2dae 100644
--- a/tests/server/test_mount.py
+++ b/tests/server/test_mount.py
@@ -972,6 +972,45 @@ class TestAsProxyKwarg:
         assert lifespan_check.count("start") >= 2
 
 
+class TestToolNamePrefixing:
+    """Test that tool names are prefixed when mounted."""
+
+    async def test_tool_name_prefixing(self):
+        """Test that tool names (not just keys) are prefixed when mounted with a prefix."""
+        # Create a sub-app with a tool
+        sub_app = FastMCP("SubApp")
+
+        @sub_app.tool
+        def my_tool() -> str:
+            return "Tool result"
+
+        # Create main app and mount sub-app with prefix
+        main_app = FastMCP("MainApp")
+        main_app.mount(sub_app, "prefix")
+
+        # Get tools from main app
+        tools = await main_app.get_tools()
+
+        # Should have prefixed key
+        assert "prefix_my_tool" in tools
+
+        # The tool name should also be prefixed
+        tool = tools["prefix_my_tool"]
+        assert tool.name == "prefix_my_tool"
+        assert tool.key == "prefix_my_tool"
+
+        # Test via client to ensure both discovery and calling work
+        async with Client(main_app) as client:
+            # List tools should show prefixed name
+            tool_list = await client.list_tools()
+            tool_names = [t.name for t in tool_list]
+            assert "prefix_my_tool" in tool_names
+
+            # Calling with the prefixed name should work
+            result = await client.call_tool("prefix_my_tool", {})
+            assert result.data == "Tool result"
+
+
 class TestResourceNamePrefixing:
     """Test that resource and resource template names get prefixed when mounted."""