树形数据源

 options:[
        {
            id: 1,
            name: '一级1',
            children: [
                {
                    id: 4,
                    name: '二级1',
                },
                {
                    id: 5,
                    name: '二级2',
                    children: [
                        {
                            id: 7,
                            name: '三级1',
                        },
                        {
                            id: 8,
                            name: '三级2',
                            children: [
                                {
                                    id: 11,
                                    name: '四级1',
                                },
                                {
                                    id: 10,
                                    name: '四级2',
                                },
                            ]
                        },
                        {
                            id: 9,
                            name: '三级3',
                        },
                    ]
                }
            ]
        },
        {
            id: 2,
            name: '一级2',
        },
        {
            id: 3,
            name: '一级3',
            children: [
                {
                    id: 6,
                    name: '二级3',
                    children: [
                        {
                            id: 12,
                            name: '三级4',
                        },
                    ]
                },
            ]
        }]

需要查询的id

test:[1,3,12]

 定义递归函数

 getTreeName(list,id){
        for (let i = 0; i < list.length; i++) {
        if(list[i].id===id){
          return list[i].name
        }else if(list[i].children && list[i].children.length>0){
            let res=this.getTreeName(list[i].children,id)
            if(res){
              return res
            }
          
         }
        }
       }

 对需要查询的id数组遍历输入结果

   getOptionsNames(){
        let newArr=[]
        for(let i=0;i<this.test.length;i++){
          newArr.push(this.getTreeName(this.options,this.test[i]))
        }
        console.log(newArr);
    }

  created(){
      this.getOptionsNames()
  },

打印结果