Timestamps (or dates or numbers) do not have any "format2. Neither in Postgres nor in Oracle or in any other relational database).
Any "format" you see, is applied by your SQL client displaying those values.
You need to configure your SQL client to use a different format for timestamp, or use the to_char() function to format the value as you want.
In particular, to get the format you desire, use
SELECT to_char(current_timestamp, 'MON-MM-YY HH.MI.SS.US000 AM');
The output format can be changed in psql by changing the DateStyle parameter, but I would strongly recommend to not change it away from the default ISO format as that also affects the input that is parsed.