First: I'm sorry for the Language and CaPitalization - but my browser seems to have som strange auto-correction setting (and my native Language isn't English either) But try to read this With the best intentions - and I'll check my browser-settings for future posts....

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I have been "coming out" in a small business. I'm in a small consulting business where we also deals With a small and close group of clients.
I can confirm that it's been a long way with a few different experiences from what my friends in larger work-places has had.
But in "the big picture" it's a a lot of similarities - over time there's much of the same issues - but we may get it at a different time and have to choose a few different approaches. But remeber that in most large worklaces people work in smaller units there too...
I also choosed an approach where I was so happy for the acceptance in the start that I accepted that they used my old name and I kept the old e-mail and so on.
I do think that it's a good thing to be adaptive (at least to some degree) - but don't do the same mistake as me and let it go on too long.
At some point you have to draw a distinct line and say that THIS is who I am and from now on I want you to respect this.
So many People are lazy - and if they don't have to make an effort they will not. And even those that are respectful to you may begin to Wonder "why should they try to remember a new name" or maybe they will start to doubt how you want to be treated or addressed.
You will have to "rip the band-aid off" at some time. Otherwise it will only lead to a big mess.
I wanted (like you) that this should go smoothly and let time work in my favor.... -But after 2 years it was finally enough for me and I just had to realize that People dindn't want to get out of their comfort-zone.
Of course you have to show a lot of understanding and be adabtable, but my point is that you have to take a stand and maybe a small "battle" at some time.
And remember when you talk to Your management (when laying out the transition plan) that even if they haven't experienced this before this isn't so much stranger than a lot of other situations they may encounter. Some people still change names when they marry, what would they do then?
Your management also has a life outside their current job. Maybe they have a sister With a diffenet sexual orientation, maybe they have worked in a big Company With a handbook for "just about everything". Maybe theyr sposes have studied something relevant in college.
But all is individually... a bit different... you have to find Your own way (unfortunately) But try to get info from all sources you can. Maybe there's some LGBT organizations thay may offer to come With you to a meeting or maybe theres some colleauge that can help.
And don't loos faith: There's a reason why they choosed to employ you in the first Place! And you are still the same!