No. William will remain "Duke of Cambridge, Earl of Strathearn, and Baron Carrickfergus" until he becomes King, when those titles will merge with the crown and be eligible for re-granting. He will just have the heir's titles added to them, and as heir's titles are more important, William will be called by the most senior one he has. If they follow the precedent of the future George V, who was titled as "Duke of Cornwall and York" before being created "Prince of Wales" William may be known as "The Duke of Cornwall and Cambridge" (Duke of Rothsay" in Scotland) until he becomes "Prince of Wales."
George and his siblings' titles will change as well: from being "of Cambridge" they will progress to "of Cambridge and Cornwall" to "of Wales" and eventually just "The Prince George, The Princess Charlotte, and The Prince Louis" once William is himself King.