The Dr title is official as soon as you've got the official letter saying that Senate has conferred the award on you. This should follow soon after any corrections are approved. You don't have to wait for graduation, which can in some cases be nearly a year later. Graduation for PhD people is very much a formality.
I changed my title with the bank, and will change it on my passport when that needs to be renewed in 3 years time. This was purely for identity purposes, so I have something on me with the Dr title. But I do not use the title outside academic needs. Day to day I'm just Mrs. My husband, also has PhD, is same: Mr for most things, but Dr for academia. He travels abroad for his (academic) work, and it's handy to have Dr on his passport at times like that.
Note I never speak to the bank, so never have them calling me Dr. I just wanted a piece of card with it on it, for convenient proof.