Hello. My name is Marc. I'm a licensed attorney and I will be happy to answer your question. First of all, I'm sorry for your loss. Unfortunately, it is unlikely you will be entitled to your boyfriend's benefits. Only eligible survivors are entitled to benefits under the Survivor Benefits Plan. Eligible survivors include spouses, ex-spouses and children, generally.
However, if there are no such survivors, a veteran could elect for his benefits to go to a "Person with an Insurable Interest." The Department of Defense defines an insurable interest as "a natural person with an insurable interest who has a reasonable and lawful expectation of financial benefit from the continued life of the participating member, or any individual having a reasonable and lawful basis, founded upon the relation of parties to each other, either financial or of blood or affinity, to expect some benefit or advantage from the continuance of the life of the retired member."
Therefore, you could be eligible for his benefits - but only if he made you a beneficiary. You might want to make some inquiries to find out if that is the case. Since you were living with him, perhaps you could locate the paperwork. Alternatively, you might inquire with his relatives. Be advised, though, that if he had children, they are most likely the beneficiaries.
I'm sorry I couldn't give you a more optimistic answer. In any event, I hope I have provided you with useful information and helped you better understand your issues and options. If so, please feel free to rate my answer, as that is the only way I can receive credit. Or let me know if you have further questions.