What I think is the issue you're experiencing is due to passing the variable "name" as a literal string instead of its value. To fix this, you need to concatenate the value of name with the destination directory. Here's the corrected code:
[file, path] = uigetfile('*.avi');
name = fullfile(path, file); % Create the full file path
CurrentDirectory = 'C:\Users\username\Desktop\Currently Working On';
copyfile(name, CurrentDirectory);
By using the "fullfile" function, you ensure that the file path is constructed correctly, taking into account the operating system's file separator. Then, you pass the "name" variable (which holds the full file path) and the destination directory to the "copyfile" function. You may refer to this fullfile & copyfile documentation.
