Why is it faster to check if dictionary contains the key, rather than catch the exception in case it doesn’t?

On the one hand, throwing exceptions is inherently expensive, because the stack has to be unwound etc.
On the other hand, accessing a value in a dictionary by its key is cheap, because it’s a fast, O(1) operation.

BTW: The correct way to do this is to use TryGetValue

obj item;
if(!dict.TryGetValue(name, out item))
    return null;
return item;

This accesses the dictionary only once instead of twice.
If you really want to just return null if the key doesn’t exist, the above code can be simplified further:

obj item;
dict.TryGetValue(name, out item);
return item;

This works, because TryGetValue sets item to null if no key with name exists.