What is the "official" steemit blog on Steemit?
What makes it "official"?
If you can answer that question then you might see why I take issue with what you are doing. I suggest until your Facebook group is actually "official" in that same sense, you change its name to avoid appearing fraudulent.
This is the same reason Twitter has verified accounts, so people can't claim to be something they are not.
Facebook also has Verified accounts. In my opinion, people see that it's not verified so it's not fraudulent in any way.
On the contrary, Facebook's lack of verification points out that your claim is, in fact, false. This is not the official Facebook Steemit group.
I don't see the point in discussing this with you further. Do as you will. In my opinion, you are misrepresenting yourself and the group.