I added a field in the button.html of billing address form
app/design/frontend/Theme/default/Magento_Checkout/web/template/billing-address/form.html
<div class="billing-address-form">
<!-- ko foreach: getRegion('before-fields') -->
<!-- ko template: getTemplate() --><!-- /ko -->
<!--/ko-->
<form id="new-billing-address" data-bind="attr: {'data-hasrequired': $t('* Required Fields')}">
<fieldset class="fieldset address" data-form="billing-new-address">
<div class="field _required full_name">
<label class="label">
<span data-bind="i18n: 'Full Name'"></span>
</label>
<div class="control">
<input type="text" class="input-text required" id="full_name_text" data-bind="event:{ keyup: fullNameChanged }" />
</div>
</div>
<!-- ko foreach: getRegion('additional-fieldsets') -->
<!-- ko template: getTemplate() --><!-- /ko -->
<!--/ko-->
<!-- ko if: (isCustomerLoggedIn && customerHasAddresses) -->
<div class="choice field">
<input type="checkbox" class="checkbox" data-bind="checked: saveInAddressBook, attr: {id: 'billing-save-in-address-book-' + getCode($parent)}" />
<label class="label" data-bind="attr: {for: 'billing-save-in-address-book-' + getCode($parent)}" >
<span data-bind="i18n: 'Save in address book'"></span>
</label>
</div>
<!-- /ko -->
</fieldset>
</form>
</div>
Copied vendor/magento/module-checkout/view/frontend/web/js/view/billing-address.js
and placed it in app/design/frontend/Theme/default/Magento_Checkout/web/js/view/billing-address.js
And then added the binded function to the billing-address.js
fullNameChanged: function() {
var fullNameValue = $('#full_name_text').val();
var firstSpacePos = fullNameValue.indexOf(' ');
if (firstSpacePos!=-1) {
//this means user has entered a space
var first_name = fullNameValue.substring(0, firstSpacePos).trim();
var last_name = fullNameValue.substring(firstSpacePos).trim();
$('div[name="billingAddressshared.firstname"] .input-text').val(first_name);
$('div[name="billingAddressshared.lastname"] .input-text').val(last_name);
}
else{
//this means user has entered a single word
$('div[name="billingAddressshared.firstname"] .input-text').val(fullNameValue);
$('div[name="billingAddressshared.lastname"] .input-text').val(fullNameValue);
}
$('div[name="billingAddressshared.firstname"] .input-text').keyup();
$('div[name="billingAddressshared.lastname"] .input-text').keyup();
}