These are both pretty bad if used non-locally across files. Maybe it's a bad habit from Java, but verbosity helps a lot,

updateDateCallback()

updateDateFromClick()

These show how it's used and what it's doing.

(actually, "up-date date" kind of irks me,)

handleDateChangeClick()

dateChangeModalClickEvent()

And what does this thing actually do? Is it updating data, or making the update UI visible? It's kind of unclear.

If you're showing/hiding UI rather than performing the model update,

showChangeDate[Field/Modal/...]()

beginChangeDateFlow()

...

Code should read kind of like a book.