How to save user input into a variable in html and js

It doesn't work because name is a reserved word in JavaScript. Change the function name to something else.

See http://www.quackit.com/javascript/javascript_reserved_words.cfm

<form id="form" onsubmit="return false;">
    <input style="position:absolute; top:80%; left:5%; width:40%;" type="text" id="userInput" />
    <input style="position:absolute; top:50%; left:5%; width:40%;" type="submit" onclick="othername();" />
</form>

function othername() {
    var input = document.getElementById("userInput").value;
    alert(input);
}

First, make your markup more portable/reusable. I also set the button's type to 'button' instead of using the onsubmit attribute. You can toggle the type attribute to submit if the form needs to interact with a server.

<div class='wrapper'>
<form id='nameForm'>
<div class='form-uname'>
    <label id='nameLable' for='nameField'>Create a username:</label>
    <input id='nameField' type='text' maxlength='25'></input>
</div>
<div class='form-sub'>
    <button id='subButton' type='button'>Print your name!</button>
</div>
</form>

<div>
    <p id='result'></p></div>
</div>

Next write a general function for retrieving the username into a variable. It checks to make sure the variable holding the username has it least three characters in it. You can change this to whatever constant you want.

function getUserName() {
var nameField = document.getElementById('nameField').value;
var result = document.getElementById('result');

if (nameField.length < 3) {
    result.textContent = 'Username must contain at least 3 characters';
    //alert('Username must contain at least 3 characters');
} else {
    result.textContent = 'Your username is: ' + nameField;
    //alert(nameField);
}
}

Next, I created an event listener for the button. It's generally considered the bad practice to have inline js calls.

var subButton = document.getElementById('subButton');
subButton.addEventListener('click', getUserName, false); 

Here is a working and lightly styled demo:

CodePen demo of this answer.