Poor Blue-Haired Lawyer. In most other episodes he would absolutely be the most prominent character to debut, but "Bart Gets Hit By A Car" we've already met Lionel Hutz and Dr Nick - two all time classics - so his arrival seems less significant.

The essential facts about him are established here in his limited screen-time: he's Burns's lawyer (although he has other clients when the plot deems it necessary), he has blue hair, and he does not have a name.
His unrevealed name is perhaps the most interesting thing about him, as the show goes out of its' way to not give him one - even referring to him only as "Burns' Lawyer" in this season 23 episode "The D'oh-cial Network":
Some theorise that his surname is either "Luvum" or "Burnham" because of the office he works at in season 14's "Barting Over":

But I refuse to accept this because it's no fun. Sorry Blue-Haired Lawyer, you didn't make partner in my headcanon.
It's more fun to me that he remains nameless and deliberately obscured. The show plays with this idea when they name Comic Book Guy as "Jeff Albertson"*, and the reaction from fans was pretty unanimously negative as far as I remember - no name reveal could compete with the silliness of hiding the name for no important reason.
His blue-hair is the sort of thing that gets subtly removed from other recurring characters (hello, Ms Hoover*), but it's such an accidently defining feature of this character (it's literally right there in his not-name!) that he gets to be on the very short list of non-Marge blue-haired characters.
Blue-Haired Lawyer's appearance is based on actor Charles Lane, and I can definitely see it:

And his voice is based on Roy Cohn, a lawyer during the McCarthy era, a early Donald Trump ally, and generally a bad person. Here's an interview with Cohn if you want to compare.
*if you have no idea who I'm talking about here, do not worry, we'll get to it...sometime.
This post is part of my "Every Simpsons Character Ever" series. For a list of my rules in this project, click here.