Surgery had nothing to do with whether I was done transitioning; I had surgery (once and final) a couple of years after I was officially done by my own standards, and after I'd been living as a woman for ~3 years.
That said, I waited until about 18 months after I started transitioning - and that was also six months after I was done, because it took me about a year to transition fully - to change my name, for unrelated legal reasons that held everything up. I waited to do the gender marker until I'd gotten the name change, too, so that I could basically deal with all the places that needed changing only once.
Yes, that means I lived as a woman with a male name and gender marker for a good six months at least, and it sucked.