Typically, a committee (or Joint Working Group) is formed from members of the International Union of Pure and Applied Chemistry (IUPAC) and Physics (IUPAP). This group evaluates all claims on potentially new elements, published prior to a given cut-off date. The group follows a given procedure and regulations. The following link provides more information, including links to the most recent publications on elements 113-118.
Here, discovery rights were granted to the so-called Dubna-Livermore collaboration for elements 114 and 116, which since then have been named Fl, flerovium, and Lv, livermorium. The names are based on proposals of those scientists having discovered a new element, and subsequently recommended by IUPAC.