SpreadsheetID	SheetName
123456789012345678901234567890123456789012345	HistName

コード.gs

function doGet() {
  var html = HtmlService.createTemplateFromFile("index").evaluate();
  return html;
}


function appendData(inputData){
  
  var spreadSheetID_write = "123456789012345678901234567890123456789012345";
  var sheetName_write = 'HistName';    
  var sheet = SpreadsheetApp.openById(spreadSheetID_write).getSheetByName(sheetName_write);

  var dataList = [];
  
  for (i in inputData){
    var approvedSet = inputData[i];
    dataList.push(approvedSet);
  }
  
  sheet.appendRow(dataList);
}

vue.js

<script src="https://cdn.jsdelivr.net/npm/vue@2.6.0"></script>

<script>  
  var app = new Vue({
    el: '#app',
    data: {
      showTemplate: 'App',
      inputName: '',
      rndNum: '',
      setAppData:[],
    },
    methods:{
      checkApp: function(){
        this.showTemplate = 'Confirm';
      },
      
      checkConfirm: function(){
        this.showTemplate = 'Thanks';
        this.setData();
                
        google.script.run
          .withSuccessHandler(function(arg){
            alert("データの登録に成功しました。");
          })
          .withFailureHandler(function(arg){
            console.log(arg);
            alert("データの登録に失敗しました。");
          }).appendData(this.setAppData);
      },
      
      setData: function(){
        this.setAppData = [];
        this.rndNum = this.createRndNum();
        
        // inputするデータ配列の作成
        this.setAppData.push(this.rndNum);
        this.setAppData.push(this.inputName);
      },      
            
      createRndNum: function (){
        var l = 12;

        // 生成する文字列に含める文字セット
        var c = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789";
        var cl = c.length;
        var r = "";
        for(var i=0; i<l; i++){
          r += c[Math.floor(Math.random()*cl)];
        }
        return r;
      },
    },
  })
</script>

index.html

<!DOCTYPE html>
<html>
  <head>
    <base target="_top">
  </head>
  <body>
  <div id="app">

  <template v-if="showTemplate === 'App'">
 
    <input type="text" id="inputName" name="inputName" v-model="inputName"></input>
    <button type="submit" v-on:click="checkApp">確認画面に進む</button>

  </template>


  <template v-if="showTemplate === 'Confirm'">
 
    <input type="text" id="inputName" name="inputName" v-model="inputName" disabled=""></input>
    <button type="submit" v-on:click="checkConfirm">登録</button>

  </template>


  <template v-if="showTemplate === 'Thanks'">
　  <p>Thanks！</p>
    <p>{{  setAppData  }}</p>
  </template>


  </div>
  </body>
  <?!= HtmlService.createHtmlOutputFromFile('vue').getContent(); ?>
</html>