Didn't Tell the Whole Truth

So basically I came clean to my boyfriend that I kissed someone else, but I lied about who it was. Now I feel bad for lying but I feel as though it's too late to mention it considering the fact that it's been 2 months since I told him about the kiss and I shouldn't have lied about it the first time. I also know that not only would he pissed to find out who it was (they are acquaintances) , but also because I waited so late to tell him. Should I just leave it be and face the guilt or should I come clean? I really love him and I don't want to lose him