The tropical cyclone name game

Dear Tom,
Has a Gulf of Mexico hurricane ever crossed Mexico and entered the Pacific?
If it did would it keep the same name?
Charles Schmitz, Burbank
Dear Charles,
It doesn't happen often, but since the advent of weather satellites in the
1960s there have been at least eight documented cases where a tropical
cyclone has traveled from the Gulf or Caribbean into the Pacific or
vice-versa. When this does occur, the storm is renamed with the next name on
the new basin's list. In 1996, Atlantic Hurricane Cesar became Pacific
Hurricane Douglas after crossing southern Nicaragua. In similar fashion,
Tropical Storm Bret became Hurricane Greg when it entered the Pacific in
1993. In 1989 Hurricane Cosme changed gender and became Tropical Storm
Allison after it survived a trip across Mexico and moved into the Gulf of
Mexico, eventually making a Texas landfall south of Houston.