Upload an image to filesystem, rename it and set it as Profile Picture for current user
I agree with @Clive you can do it that why, and also you can download the image directly with the full_name.
To do so just change the line:

$profile_pic = system_retrieve_file($picture_url, "public://profile-pictures", TRUE, FILE_EXISTS_REPLACE);


by 

$profile_pic = system_retrieve_file($picture_url, "public://profile-pictures/$full_name.jpg", TRUE, FILE_EXISTS_REPLACE);


and remove the line:

$picture-&gt;setFilename("$full_name.jpg");