Do[Pause[1]; a++, {50}]

CurrentValue[$FrontEnd, EvaluatorNames]

CurrentValue[$FrontEnd, {EvaluatorNames, "Debug"}] = {"AppendNameToCellLabel"->True}

CurrentValue[$FrontEnd, EvaluatorNames]

Dynamic[a, Evaluator->"Local"]

SetOptions[
    EvaluationNotebook[],
    StyleDefinitions -> Notebook[
        {
        Cell[StyleData[StyleDefinitions -> "Default.nb"]],
        Cell[StyleData["Input"],StyleKeyMapping -> {"Tab" -> "DebugInput"}],
        Cell[StyleData["DebugInput", StyleDefinitions->StyleData["Input"]],
            CellDingbat -> Cell[
                BoxData@FrameBox[
                    ""inspect"",
                    FrameStyle->RGBColor[0.8549`,0.83137`,0.72549`],
                    ContentPadding->False,
                    BaselinePosition->Baseline,
                    RoundingRadius->5
                ],
                "Output",
                FontSize->8
            ],
            ShowCellLabel->False,
            "GeneratedCellStyles"->{"Output"->"DebugOutput"},
            Evaluator -> "Local 2",
            CellEvaluationFunction -> (
                With[{kernel = CurrentValue[EvaluationNotebook[], Evaluator]},
                    ToExpression[
                        #1,
                        StandardForm,
                        Function[
                            Null,
                            Dynamic[#1, Evaluator -> kernel],
                            HoldAll
                        ]
                    ]
                ]&
            )
        ],
        Cell[StyleData["DebugOutput", StyleDefinitions->StyleData["Output"]],
            CellDingbat -> Cell[
                BoxData@FrameBox[
                    ""value"",
                    FrameStyle->RGBColor[0.8549`,0.83137`,0.72549`],
                    ContentPadding->False,
                    BaselinePosition->Baseline,
                    RoundingRadius->5
                ],
                "Output",
                FontSize->8
            ],
            ShowCellLabel->False
        ]
        },
        StyleDefinitions -> "PrivateStylesheetFormatting.nb"
    ]
]