It seriously depends on who came up with the ideas of the story the way i see it. if they both did than yes both of their names should be on it, but if only one of them came up with the story then that one persons name should only be on that cover.
Just the way I see it.
Here's what Wikipedia has to say:
Artist Bob Kane negotiated a contract with National Comics, the future DC Comics, that signed away ownership of the character in exchange for, among other compensations, a mandatory byline on all Batman comics (and adaptations thereof). Finger's name, in contrast, does not appear as an official credit on Batman stories or films, even the comics he wrote in the 1940s and 1950s.
Finger received limited acknowledgment for his writing work in the 1960s; the letters page of Batman #169 (Feb. 1965), for example, features editor Julius Schwartz naming Finger as creator of The Riddler, one of Batman's recurring villains.
Additionally, Finger did receive credit for his work for National's sister company, All-American Publications, during that time. For example, the first Wildcat story, in Sensation Comics #1 (July 1942), has the byline "by Irwin Hasen and Bill Finger", and the first Green Lantern story (see above) is credited to "Mart Dellon and Bill Finger". National later absorbed All-American. National's practice in the 1950s made formal bylines rare in comics, with DC regularly granting credit in its comics only to Kane; to William Moulton Marston, creator of Wonder Woman, under his pseudonym of Charles Moulton; and to Sheldon Mayer.
I'm not sure about this one... my opinion has always been that the character and the design are two different things, and that while the design does add something important, it's the history and personality of the character that actually matters. Designs and suits change from artist to artist, but the character always remains the same, at least for the most part. I've just never seen them on the same level, as the idea of the character was created before the artist makes the design.
So the question is whether or not the design makes a difference to the character and whether the artist deserves credit for that contribution... personally I would say no... but I would never call into question the time and effort that's gone into making a character look and feel the way they do... but hey, that's just my opinion
@Hunter114: well, ask yourself, would Batman be the same if that drawing up there (Bob Kane's) had remained? Finger may have not come up with the idea, but the changes he made were crucial for Batman to still exist and be as popular as he is today and as he was in the Golden Age. He made very important changes, if he didn't, the Batman we know today would be completelly different.
But that's just how I see it...
The credit for any character's creation (including Batman) should be given to both the writer(s) and the artist(s). Without one, the other would be entirely differently.
@AKA_TERMINATOR: As silly as it sounds to those of us in an age in which it's not unusual for a dozen or more people appear on a credits page, Golden Age creators were often uncredited. Sometimes the creators wanted it this way because they only worked in comics to put food on the table while they continued to look for more professional writing jobs.
Don't get me wrong, I'm not saying that there's no contribution or that what artists in general do isn't important, it's just that one of the big counter-arguments to that are characters like Hulk, Daredevil etc who's "classic" look is not necessarily their "original" look and then there are characters like Green Arrow (and others I currently can't think of) whose look is taken from somewhere else... but yeah, you do have a point and I understand your point of view... which is why I was conflicted.
The problem is when not all examples of something fit the "rule" - should all the first artists (etc) be given credit in the creation of the character or should none of them be... I don't really see a problem either way, but I'm sure others probably would.