I don't know about the US, but in the UK you can definitely say "D-Day" to mean "an anniversary of the original D-Day", not strictly 6/6/1944. It's not wrong.
Just like you can say "Independence Day" to mean July 4th of any year, not only the specific historical date on which the US declared independence.
Just like you can say "Independence Day" to mean July 4th of any year, not only the specific historical date on which the US declared independence.