Magento2 – Setting value of quote table

I have an Api endpoint from where I am fetching values like customer first/last name email, I want to store these values in quote table for customer_firstname , customer_lastname fields. However, when I am trying to set the value and save it, I find there for every value fetched and stored there is a null value stored.

      $email = $customer['Email'];
      $firstname = $customer['FirstName'];
      $lastname = $customer['LastName'];
      $quote->setCustomerFirstname($firstname);
      $quote->save();

values saved will be in quote table are :
john
Daniel
Null
Karl
abc
null
efg
null

While from the api endpoint the values coming are: john, daniel,karl, abc, efg. Could you please tell me what can be done in this case. I also tried to first set values of customer and then assign it to quote but that did not work either.