Yes, that is correct- all the records say Elias. He has a brother Thomas and it is in keeping with this family's tradition that more than one child may have the same first name (of an ancestor) but be called by their middle name. The first name sometimes serves to distinguish them from a cousin of the same name in the same area at the same time. This family used only a few first names. This is a particularly confusing line. To date I haven't found a record which includes his first name, Thomas. Birth records are hard to find for this family during this time period. So you are right, there is lots of proof for the Elias but no sources for the Thomas. There is a brother, Thomas of the same family - not to be confused with this guy. Thanks!!