Oracle stores all DATE data types as a seven digit binary. The format mask you use on insert statement has nothing to do with how it is stored.
As Agador correctly states, you use to_char to convert your date to a string and choose your format mask for display.
If you don't explicitly do this yourself, Oracle will internally call a version of to_char to convert the binary data to a string using the default date format parameter stored in the nls_database_parameter table. Usually this is dd-mon-rr by default.