I'd keep it! I think you have picked a great name and don't need to criticize yourself for not doing it differently. I personally think J. is a great middle initial. My dad and husband both use their middle initial in formal settings so I always think about how the middle initial will work and J. is almost always awesome. Alice J. Smithson. For me there is a bit of a slur with Alice M. Smithson and I prefer Alice J. Not a deal breaker of course but since you already have named her Alice J. I'd say keep it.