I totally get that "not wanting to live in two worlds" thing - it's what drove me to transition sooner than I had planned to. Because of that I was somewhat less well-planned with my process than I had expected. I didn't change my name at first, but my work was OK with that, although all my deets changed (eg email and cards, etc) for the purposes of my work they kept paying me as my old name until I sorted myself out. That's probably not the usual process so I'd suggest starting the name change before contacting HR, I don't know how long it takes where you live but it took a couple of weeks for the paper work to come through for me.
I tried to tell everyone - colleagues, family and friends - more or less within the same week prior to my transition. I said to my colleagues that if anyone outside the organisation wanted "to know about me" (ie, get the gossip) then tell them to talk to me directly instead and I would answer their questions (not surprisingly I only got one of those). As for dealing with people outside of my organisation that I did direct business with, I sent them all a personal email to let them know what had changed. In pretty much all cases they congratulated me like I was pregnant or getting married...!?! I also put a short notice with a pic of me in our company newsletter, thanking management and colleagues for their support.
There is a lot of juggling in that week or two but it starts to calm down after that.
Good luck!! 🙂
