If the code name gets out, don’t they need to come up with a new one?
No, it's not that kind of code. Mostly a nickname more than anything else. It is mostly tradition to give a "codename" to the President, VP, and their families.
The actual travel details of Presidential travel is highly classified, and they won't transmit in the open those details.
JFK = Lancer (I bet that was a bit of a double entendre)
Carter = Deacon
Reagan = Rawhide
Nancy = Rainbow
GHWB = Timberwolf (huh?)
BJ Clinton = Eagle (why?)
Hillary = Evergreen (what?)
Barbara Bush = Snowflake
Barry Hussein = Renegade
Moochelle = Renaissance (oh sure! I bet they had a real nickname for that b_tch)
Trump = Mogul
Melania = Muse