My name starts with the letter "M" and my initials are "M. L.", but in my signature I use made-up letters like "K. M." for example. Is that uncommon? I just don't like the letters of my name, but I don't want to bother changing my name legally. I don't write my whole names in my signature, just K, M and some scribbles.

Your initials are ML, pretend it stands for Melinda Lane. There's nothing wrong with writing LL, standing for Lindy Lane. So anybody who accepts your signature doesn't know if you prefer the name Kat (because your middle name is Cathy) or if your last name is maiden because you are married.
Long story short, as long as you can reproduce it to claim what is yours, there's nothing that says it has to be your initials.