If you know the file id, it is really simple,Code:

$file = file_load($fid);
file_move($file, 'public://new_file_name);

How it works:

We need a source file object to move file to the new location and update the files database entry. Moving a file is performed by copying the file to the new location and then deleting the original. To get source file object, we can use file_load() function.file_load($fid) - loads a single file object from the database$fid - file idreturn object representing the file, or FALSE if the file was not found.

After that, we can use file_move() function to move the file new location and delete the original file..

file_move($file, 'public://new_file_name)

Parameter1 - Source File ObjectParameter2 - A string containing the destination that $source should be moved to. This must be a stream wrapper URI.Parameter3 - Replace behaviour (Default value : FILE_EXISTS_RENAME)

For more details, check here.