Even in the early years of Long Island there were a lot of Smiths.  So many that it became a tradition to append their names to identify which branch of the family they came from (too bad the Carmans didn't think of it!).  Below is a short listing of who's who:

The "Rock" Smiths - Are of two branches themselves - one from western Queens County ( the Rockaway area ) which is the branch of Mordicai and the named Rockville Centre is named after, and is the older of the two.  The other is from Suffolk County and according to family lore got the name from a massive rock located on one side of their homestead near Manhasset.   Another version is that, as Judge Smith,  he was rather inflexible.   However he is also known by the name, according to his own testimony, earlier in Stamford before coming to Long Island, so you can take your choice.  Yet another variation of the story is that  Henry Smith (of Plymouth, Mass.) had a son John who in turn had as son John born in Roxbury and he was named "John Smith Rox" from where he was born to distinguish him from other family members. 

The "Nan" Smiths - There is no definitive answer to this naming.  However one author puts forward the following explanation, that there were several other Smith lines that appended their name with a contraction of where in England they originated from, and it is theorized he may have been from the area of Wales which in old times was known as "Nantzl".

The "Tangier" Smiths - Originate with Colonel William Smith, who had been the English Governor of Tangiers, in the reign of Charles the Second.  He is the founder of  St George Manor on Long Island.

The "Black" Smiths - Is a split off the 'Nan' Smith line and, as should be obvious, he was the blacksmith.

The "Blue" Smiths - So named because of a distinctive blue coat that this originator of this family branch wore. 

The "Waite" Smiths - Were so named because they were the owners of the only set of measuring weights in the area and neighbor farmers would come to them to weigh their crops before shipping them to market.

The "Bull" Smiths - According to family history, Richard "Bull" Smith got his name by riding a bull around the area now known as Smithtown and by doing so, marked the boundaries of his land grant to that area.  This branch is the most numerous.

The "Whig" Smiths - Born in Suffolk County and later moving to Pennsylvania, John Whig Smith appears to have picked up his nickname from his service in the Revolutionary War.  Being from yet another branch of the Smiths not yet having been nicknamed, there were too many John Smiths at that time to keep them apart.