An author's first and last name should only be used the first time you mention them in your manuscript. To check for this, refer to your references and use the 'Find' feature (Ctrl+f or Cmd+f) to check if you have used their full name more than once. Alternatively, as you read through the manuscript, highlight each name as you come across it; highlight the name with your curser and use the find feature as described above.
If two authors have the same last name, include their first initial in all mentions after the first. The reasoning behind this rule is to keep the text from becoming cluttered and increase readability for your audience.