Edit user's first and last name
A User's first and last name fields don't need the fields[] prefix as they aren't custom fields added to the user field group.

So using the following should work:

&lt;label for="voornaam"&gt;{{"voornaam"|title}}&lt;/label&gt;
&lt;input type="text" id="voornaam" name="firstName"
{% if currentUser.firstName %}value="{{ currentUser.firstName }}"{% endif %}&gt;

&lt;label for="achternaam"&gt;{{"achternaam"|title}}&lt;/label&gt;
&lt;input type="text" id="achternaam" name="lastName"
{% if currentUser.lastName %}value="{{ currentUser.lastName }}"{% endif %}&gt;