What would happen to a person who goes by a certain name that has nothing to do with their birth name? Like, imagine a guy name Blanko Blankerson, but everybody knows and calls him Chad to the point that no one know's his real birth name... What would happen?
I guess the same thing that happens with L, since it's just an alias, you wouldn't be able to kill them.
One of the rules used as act break bumpers in the series is that the Shinigami eyes let you see the name that is needed to kill the person.
This implies that there's only one name that will do it. It's not super-clear what would/could change the name, since aliases don't do it, but married names, not maiden names, will.
My guess is that it's basically the name a person thinks of themselves as. So, if you were in a scenario where God asked your name and you were compelled to answer truthfully, you'd say, "John Smith", and that's what could kill you. So, if your birth certificate said "Charlie Jones", but everybody knew you as "Chuck Zima", and you thought of yourself as "Chuck Zima", you'd maybe die with "Chuck Zima"...? But if you thought of that as a stage name or something, then "Charlie Jones" would still apply.
Example: Light would probably need to write in "Maurice Mickelwhite" to kill Michael Caine.