OK have googled it now! And see there are a few things it stands for. However I also googled a few other random sets of initials, and I think there will be multiple acronyms for all possible sets of initials. So unless it is something really mainstream (NHS) or something undesirable (STD) then I don't think you should let it bother you in the slightest.
Means nothing to me so I googled it and the first meaning to come up is Electronic Brakeforce Distribution! I assume you mean the other meaning though, which I don't think many people would have heard of unless they are directly affected. In fact I think EBD is preferable to BED, which you would get if you swapped the first two names - much more potential for teasing.
Depends if it is likely to become more mainstream as an acronym, I suppose. But I'd never heard of it until now.
Personally, I wouldn't do it if I were you, because you know what it stands for and it bothers you. It's your baby! All the stuff about initials not being used very much - both my Dad and my DH use their initials every day (in different professions).