1) Which name do you prefer?
"Liberty Enlightening The World" is the name of the sculpture.
"Statue of Liberty National Monument and Ellis Island" is the name of the unit within the National Park System which includes all of Liberty and Ellis Islands and the structures on them.
So, use whichever name you like. They are both correct.

2) "There are 547 registered users and only about 100 who activly participate"
As BobM correctly points out, there are many "HL Faithful" beyond those on this forum.
At the signing in St. Charles, MO, I asked BY if they had looked at Sault Ste. Marie, ONT, as a possible Reunion site. He replied that they already receive numerous complaints that HL even makes foreign lights, so they would expect to receive a lot of negative response to going across the border with a Reunion.
However, I have not noticed this "anti-foreign" sentiment on these forums, neither with respect to HL doing foreign lighthouses, nor in any responses in the Reunion forum to the post I made which included SSM, ONT, as a possible site.
So, it would appear that the overall collector response can vary considerably from what shows up in these forums.

FrankB