Weren't you suppose to discuss with your legal department about trademark issues with using the Satoshidice name? Satoshidice was pretty much the very first dice site ever created on Bitcoin network and it was very successful and sold for a huge sum back when Erik sold it. Its a piece of pioneer work in the bitcoin history.
Hence by reusing the name you are creating confusion because people might watch that Netflix bitcoin documentary which mentions Satoshidice, then go Google it and find your site and think its the same. I see some legal issues with this.
Yes we are thinking about that also. Once the site is stable in terms of user traffic, we might consider switching to another name, as changing name and domain would require additional fundings to be done.
You can't run a website under a trademarked name to build up a userbase and then in the future switch to a different name. Because a portion of your userbase would be based off the Satoshidice name alone. Hence there would be punitive damages there alone which the other partys lawyer would argue.
Domain names these days are VERY cheap it can't be one reason why you decide not to switch. Also all you need to change is pretty much the logo, leave everything else the same.
There was someone already that was confused a few posts above and said he assumed this was indeed the original Satosidice.