next-auth: Updating session.user values after form submission without relogin in Next.js project

I have a Next.js project, and I use NextAuth for authentication. In the header, when a user is logged in, the user's first and last name are displayed, as shown in this code:

import { useSession } from "next-auth/react";
export default function Test() {
  const { data: session } = useSession();
  return (
    <div>
      <h2>{session.user.firstname}</h2>
      <h2>{session.user.lastname}</h2>
    </div>
  );
}

There is a section where the user can change and update their first and last name using a form. After submitting the form, the database is updated, but the values of session.user still reflect the old values unless the user logs out and logs in again.

[...nextauth].js file codes :

import NextAuth from "next-auth";
import CredentialsProvider from "next-auth/providers/credentials";

const SECRET_KEY = process.env.JWT_SECRET_KEY;

export default NextAuth({
  providers: [
    CredentialsProvider({
      name: "credentials",
      async authorize(credentials) {
        // Connecting to the database and verify password
        //...
        const returnObject = {
          firstname: user.firstname,
          lastname: user.lastname,
          email: user.email,
        };
        return returnObject;
      },
    }),
  ],
  callbacks: {
    jwt: async ({ token, user }) => {
      user && (token.user = user);
      return token;
    },
    session: async ({ session, token }) => {
      session.user = token.user;
      return session;
    },
  },
  secret: SECRET_KEY,
  jwt: {
    secret: SECRET_KEY,
    encryption: true,
  },
  session: {
    jwt: true,
  },
  pages: {
    signIn: "/auth/login",
  },
});

How can I update the value of session.user without the need for the user to log in again so that the new values are displayed in the header section?

You can use the update(data?: any) method from the useSession() hook to update the session on the client-side without reloading the page:

const { data: session, update } = useSession();

Then, after updating the values in the database you can use this update method to update first and last name in the handle submit function:

 await update({ firstname, lastname });

After that, you need to update the sesion on the server-side using the trigger: "update" option:

async jwt({ token, trigger, session }) {
  if (trigger === 'update' && session?.firstname && session?.lastname) {
    token.firstname = session.firstname ;
    token.lastname = session.lastname;
  }

  return token
}

For more details, do not forget to go through the docs.