I started using my new name 1 month after realizing I was trans and within a week of finding/selecting it. I applied for it to be legally changed two and half months after I realized I was trans, and after a month had the court order in hand. Two months later I'm still updating websites, professional organizations, transcripts etc.
I've been fast tracking my transition because as much as I disliked who I was before I abhor the intermediate stage. Which is odd considering how much I do on campus for trans-education and making myself the person that others can ask the personal questions to.