Did you talk to anyone at work? A good first step is to have a face to face meeting with an HR representative and ask about their policy. This will give you a feel about company culture and policies.
In my case it went extremely well as the HR director I spoke to brushed it off as not much of a big deal then said I just need to notify them when I'm going to present full time in my new gender at work. Name change, gender marker on ID not a big deal either. I do have to change them on my government issued ID first though. It helps that we have a very strong anti discrimination policy and we have a sit down with the lawyers every year or so to remind employees.
You can then proceed to come out to your direct supervisor and other coworkers as you see fit. In my case I'm going to have the conversation with my manager in a couple of weeks, but I've told my closest team mates already so they aren't too alarmed by changes.