In this case, the first sentence is better. Here, "including" introduces an adverbial modifier that makes it clear which details you should provide. "Which" would indicate a noun modifier, which
would indicate that the details themselves include the name and address. This isn't quite right--the name and address are
details, they are not included by the details.
"That" would be incorrect as well, because that is used for essential modifiers. This means that it is used to narrow down the scope of what we are referring to:
The car that I want is over there.
The group that won the prize went out to celebrate.
Here, we are differentiating the particular car or group in question from other cars or groups. That wouldn't be appropriate in your example.
I also recently addressed some "which"-related concerns in another post: appositive-vs-relative-clause-117298.html#p950375
I hope this helps! Let me know if you have other examples or questions.