var a = ['a','b','c'];
var b = [
    {name: 'a'},
    {name: 'b'},
    {name: 'c'},
    {name: 'd'}
]

let arr=[];
b.forEach(v=>a.indexOf(v.name)!==-1 && (arr.push(v.name)));

两层循环

for(var i = 0 ; i< b.length ; i++){
    for(var j = 0;j < a.length ; j ++){
        if(b[i].name == a[j]){
            console.log("可以去除，也可以进行其他的操作")
        }
    }
}

b = b.map(function (obj) {
    if (a.indexOf(obj.name) >= 0) {
         console.log(obj.name);
    }
    return obj;
});

两个数组对象对比，去除相同ID的值

let arr1=[{id:1,name:'网'},{id:2,name:'二位'}]
let arr2=[{id:1,name:'问问'},{id:3,name:'多少'},{id:44,name:'多少'},{id:45,name:'多少'},]

let add=arr2.filter(item=>!arr1.some(ele=>ele.id===item.id))