为什么填写字段时我的错误消息不会更新？(React)

import React, { useState } from 'react';

const Form = () => {
  const [name, setName] = useState('');
  const [errorMsg, setErrorMsg] = useState('');

  const handleInputChange = (e) => {
    setName(e.target.value);
    setErrorMsg('');
  };

  const handleSubmit = (e) => {
    e.preventDefault();

    if (name === '') {
      setErrorMsg('请输入姓名');
    } else {
      // 处理表单提交逻辑
    }
  };

  return (
    <form onSubmit={handleSubmit}>
      <input type="text" value={name} onChange={handleInputChange} />
      <span>{errorMsg}</span>
      <button type="submit">提交</button>
    </form>
  );
};

export default Form;