There are several reasons (very specific, very compelling reasons) why the man/creature/alien/thing known as 'Undertaker' is such a popular choice among no-good doers when it comes to things such as medical expertise and service of the unusual and/or incredibly illegal kind.
First off, there's the fact that he's untraceable. Consumers of his services are hardly wont to partake in sharing the secret of his second business for… various reasons, and those who do never find it a good idea to go about alerting law enforcement of any kind about it, because that is stupid. And when it comes to the black market and mafia, where many of Undertaker's customers happen to come from, stupidity is always lethal, always devastating, and usually unwise. Even rumors of him are scarce, present in only the most inner of inner circles. (Yes, there is the fact that an innermost circle of inner circles imply that these circles go on forever, but be assured, they are very penultimate as they come.)
Word of mouth is an excellent way to learn of his services, from whispers passed discreetly at meetings or parties, to spies sent by the more affluent (read: filthy freaking rich) to discover his deeds while incognito, but to actually find the man (creature/alien/you get the idea now) is an entirely other question. Often searches to find the elusive black market doctor involve dealings with shady, dangerous people, solving obscure riddles hidden in the most random and unthinkable of locations, and giving up a butt load of cash. By the time most future clients find him in that old, dusty, obscure, and absurdly poorly lit funeral parlor he runs as a day job, they are run ragged, at least metaphorically, and are thinking that he, after all this fuss, better damn well deliver. Which he does, but that will come later. The point is, he is ridiculously hard to find.
And to track him? To catch him in the act? To get anything out of him that will get any single one of his dear customers arrested or in trouble (at least, of the kind concerned with by the court of law) at all? Even more so.
There is never any proof of Undertaker's crimes, see. Well, there is evidence, per say, especially if the crime in question is something noticeable like plastic surgery or the attachment of a green limb (not that anyone has ever asked him to do that… yet…), but never anything that ties the creepy mortician to it. "Whaaaaat?" He usually says to any officer dumb enough to accuse him or attempt to get him to confess. "You think little old me has anything to do with that poor man who exploded the other day? Do you have proof? No? Then please leave; you're making my guests quite uncomfortable."
Hahahahaha. Hilarious.
Moving on.
Reason number two happens to be that Undertaker is uncannily competent in his profession. All three of them, in fact; never a day will go by that he neglects his work, whether it be cleaning up a corpse for its funeral, performing an operation to save (or ruin) someone's life, or telling a jealous business man what exactly his wife has been doing on those rather long and suspicious vacations of hers. He is always working, and the doctor will always take on a job that tickles his fancy (or him), although sometimes doing that takes a great deal of encouragement in the form of money (doesn't work too well), begging of monumental proportions (if he finds it funny), or jokes (if they make him laugh).
Once he takes on a task, however, rest assured, he will know just what to do. He seems to have a solution to every problem, and a means to getting his hands on them as well; having people, many of whom are powerful in several aspects, owe him favors helps him quite a bit. When it comes to talking the talk, he can talk so well that he can converse quite freely with even the dead. (And they answer back, too.
And last of all, know this: Undertaker always delivers. If he takes on a job, he will finish it, and, in the eloquent words of many a client, 'very damn well deliver'. Always.
No matter what the cost… or consequence.