You can use JavaScript DOM APIs to create a new name field and use that field for name on your registration page.
step 1: create an input field for name
var input = document.createElement("input");
input.type = "text";
step 2: Append the input field to your registration form
document.getElementById("your registration form id").appendChild(input);
Now you have extra field available on your registration form which you can use to extract name value and send it to API as post data along with other field values.
Let me know if you need any other help in this.
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