I am with a payroll company who is going to file W2s for the part of year I was with them. Can two W2s be filed under my identification number with the state of NJ? How can two
W2s be filed under the same number? What is the Annual Reconciliation they keep talking about?

If the company was bought or merged, then two W-2s are needed, one each for the different EIN the old and new company has, even though the company name stays the same.

Conversely, sometimes companies do not change EINs, but DO change the company name. They generate two separate W-2s with diffrenet company names in this case.