@gia:
I understand the title change, but not the excuse that everyone keeps mentioning. What I suspect is that FUNimation foresaw a possible copyright infringement by using the name "CONAN" in bold print on the cover. Do to Dark Horse already publishing a "CONAN" series comic book. That, or perhaps the holder of the Arthur Conan Doyle estate didn't consent for whatever reason. I believe the company brought this conflict to the attention of the Japanese copyright holder and they then came up with the Case Closed title.
This theory makes more sense then the Japanese company demanding the title change. Why would they have a problem with a title like Detective Conan that is so easy to translate to English? It's not as if it was a title such as Shakugan no Shana.
 
I still suspect that the "Name" changes were actually the US companies ideas. Part of my evidence is that the name changes aren't consistent. Both VIZ and FUNimation often use different names in their publication of the series. Case in Point. There are two characters that were introduced in the manga in the same volume. Detective Miwako Sato and Inspector Ninsaburo Shiratori in Volume 21 of Case Closed. I was at the bookstore today and looked it up. In this volume, Sato's name was completely unchanged, but Shiratori was renamed "Inspector Santos". Sato in the comics plays a much larger role in the series then Shiratori. There are numerous story arcs dedicated to the love story between Sato and Detective Takagi (who's name was also unchanged).

Also, in the manga. They renamed two of the big villains in the series from Gin and Vodka to Melkior and Kaspar. How the hell are those names more easy for a US audience?? 
The whole theme in the Japanese version is that all the bad guys, The Black Organization, are code named after liquors. Gin, Vodka, Vermouth, Chianti, Kir, Korn, Sherry, Bourbon. There is currently a character that is suspected of being Bourbon in the Japanese publication. No one knows yet what Bourbon really looks like. There are often scenes showing this person who the manga is implying might be Bourbon drinking bourbon with close ups of the bottle.
Often times when Conan is thinking about this villain he has yet to meet and there is an image of a bourbon bottle in the panel.

If these name change choices were coming from the behest of the Japanese company. They should match in both forms. FUNimation alters everyone's names, but uses the proper names on the DVDs' subtitles(so I hear). VIZ changes many of the reappearing cast names, but leaves the names of the suspects alone. FUNimation changed the names of the three kids from Conan's class completely, but I hear VIZ only changed their first names and left their last names alone. 
Supposedly, VIZ followed FUNimation's lead so there would be some consistency, but there really isn't any.
 
As with One Piece and 4Kids. Just because a Japanese copyright holder signs off on a change. That doesn't make it good or right. 4Kids removed entire canon story arcs, but they must of gotten some level of consent to do such drastic editing. What VIZ is doing to the Case Closed series is similar. Yes, FUNimation also makes a lot of changes as well, but I'm currently looking in to confirm that the DVDs' subtitles actually use the Japanese names. A relative of mine is renting two of the movies for me off Netflix so I can confirm this.

@gia said:

"   ...That said, I wanted to throw out something I remember Carl Horn saying at Dark Horse: I assume that they would make some changes at the behest of a creator, but he told me that they have no interest in editing any aterial from Japan. He thinks it's disrespectful to license something and then say to the creator that some aspect is somehow unacceptable to western audiences.   Again, this doesn't cover changes made at the behest of the Japanese licensors and creators, and they want to make as much money off of their works as possible too, but I thought it was an interesting stance and thought some of you might have thoughts on it.    "

Then don't blame people when they don't want the altered product and turn to things like scanlations and fan subs.
 
It's the simple theory of economics. Supply and demand. If the supply doesn't meet the demand. People will go where they can.  You can't put out an altered and inferior product and wonder why no one wants it. Naruto, Bleach, and One Piece are selling well, because they are far closer to the original.

I seriously doubt the name changes in Case Closed/Detective Conan were initiated by the Japanese copyright holder. More likely the US licensors asked permission for these changes and got them. If these changes were something that the Japanese companies were demanding. The changes should be consistent.
There is one case in the series that makes me suspect that Gosho Aoyama isn't very happy about the changes. Though it's more speculation.

@Konanda: 
I have not seen the evidence that it was the Japanese copyright holders that demanded the name changes. What I saw was an article talking about the "title change". Even that didn't say that it was requested or demanded by the Japnese copyright holders. Just that there was a legal consideration. I suspect that it was the owners of the Dark Horse comic title of "Conan" that challenged the title, or FUNimation thought there would be a problem and contacted the Japanese company to create a new title.
Don't you find it just a bit odd that a series called "Detective Conan" , such a simple and straight to the point title, in Japan was changed to "Case Closed"? It's not as if it is some overly Japanese sounding title, such as Shakugan no Shana, Seto no Hanayome, or Nagasarete Airantou.

Titles really don't matter in the grand scheme of things. If One Piece was renamed Pirate Adventures. As long as the story isn't changed it matters little. It would still be One Piece.

The facts are that the name changes aren't consistent. At times FUNimation uses one name and VIZ uses another at times.
 
For example, two of the major villains in the series are codenamed "Gin" and "Vodka", but in the Case Closed manga version they are called "Melkior" and "Kaspar" (seen in Volume 4). How are these two names more English friendly? You can't say that it was because the names are liquors. They kept Haibara, old code name "Sherry". Not to mention that this is a murder mystery series where they talk about all kinds of poisons and way to kill others. I don't see how you could think it would be alright to read and see graphic crime scenes, but it somehow be beyond the pale to read the names of liquors.
Even in the FUNimation DVDs I've been hearing the Japanese with subtitles keeps their Japanese names. (I'm currently looking into it to see if FUNImation also renamed Gin and Vodka.) FUNimation offers an alternative for the original names. VIZ offers none.
 
Further, two of the police officers in US manga series keep their original Japanese names in the VIZ publication for some reason. Their names are Takagi and Satou (Satou was introduced in Volume 21). They are reappearing characters.
 
Another much more dramatic alteration that isn't at all consistent between VIZ and FUNimation. A major character who was introduced in Volume 18 of the manga is called Ai Haibara, real name Shiho Miyano. In VIZ she is renamed Anita Hailey, but FUNimation reportedly renamed her Vi Graythorn. Don't you think these two different names would "confuse readers"? She's not a minor character at all.

If the name changes were demands from the Japanese company. They should be consistent in both versions. There is no reason for them to tell FUNimation to use one set of names but tell VIZ to use others.

I'm sure the copyright holders consented to the alterations that 4Kids did to One Piece, and that was utter butchery. Entire canon story arcs were removed, skin colors were changed, tattoos were removed, guns were replaced with squirt guns, and cleavage lines were erased. It didn't make it right or good. What VIZ is doing to Detective Conan is equivalent to what 4Kids did to One Piece. I can even show a scene where the translation for one case was wrong in the VIZ publication.
 
What I'm saying is that if you are going to change series to ways they were not intended and you are altering the "story". Don't then complain when people don't want to buy it and go to scanlations or fan subs. That's the risk you take when you make such drastic alterations, and refuse to offer an alternative. I, personally, would of never known what  the real One Piece anime was like if I hadn't found the fan sub sites. Though, now that FUNimation's website is posting One Piece subtitled and no real seen editing. I wont watch fan subs again. Hell, I haven't been on a  fan sub site at all since I discovered FUNimation's video site and selection. There is no reason to go anywhere else.