I feel that you should think about what your discission would mean to your life five years from now. Will you be still hiding your gender identity and pretending that you are some one you are not. You are at a transition point in your life. You are writing your life's story when you make your decisions. If it is possible for you to start legally putting in to your official history your chosen name and your gender identity, you may be able to graduate from graduate school and gain employment as who you really are. I really don't know how coming out will affect your gaining entrance into graduate school and getting a job afterwards. But what I do know that finally acknowledging to myself that I was really a woman at 53 years old that up to that time my life's history had stamped me as a male. All of my educational history from kindergarten to my Master's degree has male stamped all over it. I had 25 years of teaching heaven knows how many children with a male's gender identification stamped all over it. I had been married for 25 years and fathered 5 children, four of them adults, who had only known me in my male identity. On the job for the next eleven years I taught still taught school with a male identity while in my home life with my immediate family I presented myself as my female self. It wasn't until the last year or two that I changed my Facebook identification to female, my name to Michelle (Mike) H........, and posted a picture of myself as my female self. I was out to all of my children, old friends, and students, many of which had been my kid's personal friends, and had been in my family home many times. I dress as you see in my picture when I go to my present children's school dressed like you see in my profile picture.
With all of this history, plus the fact that male hormones have left my physical characteristics with male characteristics, I have to accept that no matter whatever changes I make to my body, I am out as a trans woman. I will never expect to pass as a cis woman, because too many people know my history. I have 67 years as a legal labeled male, to have everything changed to female, even if I take hormones, have surgery, and have all my current legal documents changed.
My point being, that if coming out to your graduate school means that you can't get into any school or permanently damages your chances to get a job in your chosen field, then for survival purpose, there is a good argument for you staying in the closet. On the other hand balance it with the fact that every day you are in the closet you create more of a history as a person you aren't, and it makes it harder to change and disappear into the your the gender that you really are. Either way its a gamble. If you are extremely talented in your chosen field its highly likely that there are employer's in your field that will find you indispensable and coming out on the job will just be a convenience. However, if there are lots and lots of competition for each job in your chosen field, getting your first job and keeping it may be difficult if your employer becomes aware that your transgender, and you will be stuck in the closet for years or unemployable.
Only you know, what your own personal emotional needs are. If you can't live with staying in the closet for years, then it is better to deal with it now and find a graduate school and a profession where being a transgender is not a problem. However if you can stand living in the closet the next 5 to 10 years because that is probably how long it will take for you to become established in your field and gain enough credit with your employer's that your being transgender is not an issue for them, then stay in the closet.
I really can't make your discission for you. I know that for myself, I was thirteen, when I first realized that I identified more with being a female, then I did with being a male. Because at that age and at that time, 1959, I saw no way of transitioning to my female self and surviving to old age, I discided to put it off until I was much older. When I was older, I realized that yes trying to be a male all these years did insure that I had an income on Social Security that was livable and could then transition with an income, I had sacrificed 40 years of living as my female self. I had lost the chance to a body that was more naturally female because I had not taken female hormones when I was young and male hormones had damaged my female body. I had lost my chance to pass as a woman with anybody ever suspecting that I had been born with a male body. For practical purposes I will be accepted as a trans female, or at the very least as a male who cross dresses 24/7/366, leap year. I just keep being my female self, and hope that other's will give up with their insistence that I can never be a true female.
Whatever your chose is, there are no wrong choices, only choices we can live with, and choices we can't live with. When we can't live with our choices, then we modify it somehow, so that we can deal with it. I just came to the point in my life when I had to accept that I was not a man and had never been one, and I had to give it up and be my female self, and accept the consequences of waiting to long. It really doesn't matter what others think about me, because I can't change that. For me the worst thing for me to do was to try and hide my female self period. I had to be my female self even when it might be awkward for myself and the people around me. No one has threatened my life or shown any visible anger, though, I find that am not crowded on the city buses I ride because because people chose not to take the empty seat next to me except when the bus is crowded. This works for me.
