How to add data from a client-side input field to my array websites[name] and then display it in html document

The first step to solve your problem is to implement some kind of saving. A simple yet stable solution is to utilize the Node's filesystem API. Instead of storing your websites in a variable (which makes them refresh with every session), you should modify the file. As it was already pointed out in the comments, JSON is a good starter for such things. Here is my code (for the sake of simplicity, I used the synchronous variants, you can replace them with async + callback if you wish):

import fs from "fs";
function getWebsites() {
    // Open the file and read the content
    const data = fs.readFileSync("./websites.json", "utf-8");
    return JSON.parse(data);
}
function updateWebsites(name) {
    const content = getWebsites();
    content.websites.push({ name: name, enable: true });
    // Write the modified data and close the file
    fs.writeFileSync("./websites.json", JSON.stringify(content));
}
server.post("/last", (req, res) => {
    var DataG = req.body.name;
    updateWebsites(DataG);
    // ...
}

Later you can implement some kind of caching to prevent redundant calls of readFileSync() until something has changed. Moving on to the second part of your idea: you can modify the HTML file with each website list update, but a way more typical way to reflect the data state is to add another endpoint to your server:

server.get("/sites", (req, res) => {
    res.statusCode = 200;
    res.send(getWebsites());
});

Having this set up, the only thing you have to do from your client is to query the list:

    async function displaySites() {
        const res = await fetch("http://localhost:3000/sites");
        const data = await res.json();
        const container = document.getElementById("somecontainer");
        data.websites.forEach(el => {
            const paragraph = document.createElement("p");
            paragraph.innerText = el.name;
            container.appendChild(paragraph);
        });
    }
Display websites