If I wanted to sell an iphone game in which you play as a famous person, would that require permission from the famous person?
Now just as a heads up, we aren't lawyers and you shouldn't take advise from a forum website as legal advise.
Now to answer your question: most likely
It really depends on where you live and which laws govern it for any game. Such that if you live in India, you would need to look at local law.
Being released on iOS, you typically would also need to adhere to US law since Apple is based in the US.
So let's look at one fairly relevant example. In this case they won the lawsuit for using "likeness" without permission. That means that even without using their name, the characters in-game were close enough to their real-life counterparts that EA was forced to fork a lot of money.
Now let's look at a more recent example. In this case Lindsay Lohan is suing in a very similar fashion. Now if I remember correctly, this one never went anywhere. However is goes to illustrate that people being people will get upset when they aren't paid.
Now on the flip side of the matter is publicity. A small-time game may be able to get away with it. "If nobody knows, then nobody will sue me" is unfortunately too common. Although in case a game gets big, suddenly you get noticed, and likely shut down or sued.
Depends on factors such as whether you're making money (and who for), whether it's a parody, what country's laws apply, etc.
A parody game making money for charity in a country with very strong fair use doctrines is going to be different to an academic venture in a country without a concept of fair use.
We are not lawyers; ask a lawyer.
In short, ABSOLUTELY!
It's basically the same as stealing their name and everything they've worked for to say that they like and want to sponsor your game, when they probably don't.
Your best bet is most likely to make a character that looks similar without being an exact replica, then change the first name. This way you have a character that reminds your players of the famous character without actually using the famous person. It's not guaranteed to keep you from being sued but it's a much better option than using the person without permission.