It depends. If the shortened name is what they prefer, so be it. Vice versa as well.
Say I had a daughter named
Beatrix and her friends and family call her
Trixie at times. Whether she wants to be called
Trixie as her everyday name is her choice as soon as she’s old enough. If she wants this, I’ll introduce her as
Trixie. If she prefers only close ones calling her that name or something like that I’ll introduce her as
Beatrix.
https://www.behindthename.com/pnl/217493
"It is not in the stars to hold our destiny but in ourselves." - William Shakespeare