Guilty (Aussie) as charged!
We would very likely shorten but even here, there are people who are able to insist on full names; and the trend seems to be as in UK, where it’s less assumed your kid will be OK with nicknames - my 17 year old nephew for eg is always Att1cus, because he parents exclusively call him that and he’s never suggested anything else. My daughter (9) gets her full name only from her friends. I’m guessing that’ll change in a few years but it’s not as likely as it was in my generation and for now she only gets nicknames at home. She has several full name friends - including Charlotte & (four syllable) Amelia. The parents can really set the rule - until the kid starts to enjoy nicknames with their friends. But even then the parents’ naming pattern has a long reach.
US even more likely to be able to set exception of full name - and fortunately, if a nickname is intuited at all, Dot is one of only a few likely nicknames for Dorothy and it’s super cute and ages really well. I personally love when it’s say 60% the full name & 40% nickname but you could go for and assert a different ratio. Good luck!