Even if your name is something like Elizabeth and 'Liz' would be reasonable or indeed Thomas to 'Tom'. Not as in Charlotte to 'Lottie' - I can't exactly articulate why but I find the latter unreasonable.
My name is a bit of a silly 'made-up' name if you like. I'm named after a capital city so when people shorten it it ends up sounding even more ridiculous.
But do you make a point of saying "Well actually can you call me xxx please" even for your dc?