flight following is only "flight following" which means the controller will issue traffic advisories as his workload permits. you've got to remember your still flying 'VFR" and are still responsible for your own safety and separation... aircraft flying IFR receive priority handling over any flight following advisories you might receive as a VFR aircraft...
Also to answer your question, does the tower know who I am when being transferred to the tower during flight following "NO" all the controller did was cancel your flight following and advised you to maintain 'VFR" and contact the tower on whatever frequency he gave you...