Conventionally, western names have the given name first, any second or subsequent names and then the family name. So, my initials are MDS. From what you say, you would use the initials XL if dealing with westerners.
I see no reason why you could not choose the initial characters of each of the Kanji sounds to make up a set of western initials, but if you did, you may find people asking you what your middle name is.