This depends on when and where in history you are talking about.
During the 20th century in the USA the most common full name for a
Jerry would have been
Gerald.
Back in the 18th and 19th century in
Ireland it would probably have been
Jeremiah, and
Jeremiah itself would have been the "English" name replacement for the Irish name
Diarmaid.
Jerry has also been the most common pet form of
Gerard and
Jerome in the 20th century, but usually neither of those was as common as an official name as
Gerald was.