Trying to check if any checkbox on the page is checked

I want to check if any checkbox on the website has been checked when text has been entered in the name text box. I know that the EventListener works for name since this works without the document.getElementsByName("event[]").checked, but how do I make it work for the checkboxes?

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<!-- language: lang-js -->
document.getElementsByName("name")[0].addEventListener('change', (event) => {
if (event.target.value.length != 0 && document.getElementsByName("event[]").checked ) {
window.alert("checked");
}
})

<!-- language: lang-html -->

<form id="bookingForm" action="javascript:alert('form submitted');" method="get">
<section id="Events">
<h2>Select Events</h2>
<div class='item'>
<span class='eventTitle'>Event number 1</span>
<span class='eventPrice'>10.50</span>
<span class='chosen'><input type='checkbox' name='event[]' value='1' data-price='10.50'></span>
</div>
<div class='item'>
<span class='eventTitle'>Event number 2</span>
<span class='eventPrice'>5.00</span>
<span class='chosen'><input type='checkbox' name='event[]' value='2' data-price='5.00'></span>
</div>
<section id="Cost">
<input type="radio" name="delivery" value="ticket" data-price="10">
<h2>Total Price</h2>
Total Price <input type="text" name="total" size="12">
<p>Name<input type="text" name="name"></p>
</section>
<p><input type="submit" name="submit" value="Book"></p>
</section>
</form>

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I'd suggest:

document.getElementsByName("name")[0].addEventListener('change', (event) => {
// here we used event.target.value.trim.length in order to guard against
// white-space strings being considered valid (if that's not a problem
// then the trim() method can be removed), and also we used:
// document.querySelector() to find the first of any <input> element
// with a type equal to 'checkbox' which is also checked;
// document.querySelector() returns either the first such element or null:
if (event.target.value.trim().length > 0 && 
document.querySelector('input[type=checkbox]:checked') !== null) {
window.alert("checked");
}
});

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<!-- language: lang-js -->

document.getElementsByName("name")[0].addEventListener('change', (event) => {
if (event.target.value.trim().length > 0 &&
document.querySelector('input[type=checkbox]:checked') !== null) {
window.alert("checked");
}
})

<!-- language: lang-html -->

<form id="bookingForm" action="javascript:alert('form submitted');" method="get">
<section id="Events">
<h2>Select Events</h2>
<div class='item'>
<span class='eventTitle'>Event number 1</span>
<span class='eventPrice'>10.50</span>
<span class='chosen'><input type='checkbox' name='event[]' value='1' data-price='10.50'></span>
</div>
<div class='item'>
<span class='eventTitle'>Event number 2</span>
<span class='eventPrice'>5.00</span>
<span class='chosen'><input type='checkbox' name='event[]' value='2' data-price='5.00'></span>
</div>
<section id="Cost">
<input type="radio" name="delivery" value="ticket" data-price="10">
<h2>Total Price</h2>
Total Price <input type="text" name="total" size="12">
<p>Name<input type="text" name="name"></p>
</section>
<p><input type="submit" name="submit" value="Book"></p>
</section>
</form>

<!-- end snippet -->

It's worth adding that your first line could be potentially simplified a little using document.querySelector() rather than using indices:

document.querySelector("input[name=name]").addEventListener('change', (event) => {
if (event.target.value.trim().length > 0 && 
document.querySelector('input[type=checkbox]:checked') !== null) {
window.alert("checked");
}
});

<!-- begin snippet: js hide: true console: false babel: false -->

<!-- language: lang-js -->

document.querySelector('input[name=name]').addEventListener('change', (event) => {
if (event.target.value.trim().length > 0 &&
document.querySelector('input[type=checkbox]:checked') !== null) {
window.alert("checked");
}
});

<!-- language: lang-html -->

<form id="bookingForm" action="javascript:alert('form submitted');" method="get">
<section id="Events">
<h2>Select Events</h2>
<div class='item'>
<span class='eventTitle'>Event number 1</span>
<span class='eventPrice'>10.50</span>
<span class='chosen'><input type='checkbox' name='event[]' value='1' data-price='10.50'></span>
</div>
<div class='item'>
<span class='eventTitle'>Event number 2</span>
<span class='eventPrice'>5.00</span>
<span class='chosen'><input type='checkbox' name='event[]' value='2' data-price='5.00'></span>
</div>
<section id="Cost">
<input type="radio" name="delivery" value="ticket" data-price="10">
<h2>Total Price</h2>
Total Price <input type="text" name="total" size="12">
<p>Name<input type="text" name="name"></p>
</section>
<p><input type="submit" name="submit" value="Book"></p>
</section>
</form>

<!-- end snippet -->

References:

• CSS:
• Attribute-selectors ([attribute=attribute-value]).
• :checked.
• JavaScript:
• document.querySelector().
• String.prototype.trim()

//--Get all checkboxes, you can have another way of fetching checkboxes
var checkBoxes = document.getElementsByTagName("input");
//--For each checkbox, check if it is selected
for (var i = 0; i < checkBoxes.length; i++) {
if (checkBoxes[i].checked == true) {
alert('checked');
}
}

Use document.querySelectorAll to get an array containing all the checkbox inputs in the document:

var checkboxes = document.querySelectorAll("input[type=checkbox]");

Then, to check if any of the checkboxes are checked:

var anyChecked = false;
for (var i = 0; i < checkboxes.length; i++) {
  if (checkboxes[i].checked) {
    anyChecked = true;
    break;
  }
}

Alternatively, if you want an array containing only the checkboxes that are checked, you can do the following:

var checkedCheckboxes = checkboxes.filter(checkbox => checkbox.checked);

document.getElementsByName("name")[0].addEventListener('change', (event) => {
if(event.target.value.length !== 0) {
// Get all checkboxes  
const checkboxes = document.getElementsByName("event[]");
for(i=0; i<checkboxes.length; i++) {
// Check if checkbox is checked or not
if(checkboxes[i].checked) {
window.alert("checked");
}
}
}
})