You refer to the module with three different names, Logger, Logg, and MyLib::Logger. If you're not getting an error about a failed use of Logger, then Perl's loading it from a file named MyLib/Logger.pm, but MyLib/ is in @INC.

Because that's how use loads it, Perl will try to call Logger->import( 'data_log' );. There's no failure if this import fails to exist in the package. Your package is MyLib::Logger, which does have an import but which doesn't get called, because its name doesn't match the name by which Perl loaded the file.

Short answer: change package MyLib::Logger; to package Logger;. (Also change the comments for the sake of other people reading the code.)