Refresh page and run function after JavaScript

You need to call myFunction() when the page is loaded.

window.onload = myFunction;

If you only want to run it when the page is reloaded, not when it's loaded for the first time, you could use sessionStorage to pass this information.

window.onload = function() {
    var reloading = sessionStorage.getItem("reloading");
    if (reloading) {
        sessionStorage.removeItem("reloading");
        myFunction();
    }
}

function reloadP() {
    sessionStorage.setItem("reloading", "true");
    document.location.reload();
}

DEMO

function myFunction() {
    document.getElementById("welcome").textContent = "Welcome back!";
}

window.onload = function() {
    var reloading = sessionStorage.getItem("reloading");
    if (reloading) {
        sessionStorage.removeItem("reloading");
        myFunction();
    }
}

function reloadP() {
    sessionStorage.setItem("reloading", "true");
    document.location.reload();
}

DEMO: https://jsfiddle.net/barmar/5sL3hd74/