According to the United States Patent and Trademark Office (USPTO), the trademark for The Last Guardian has been abandoned by Sony.
Mark: THE LAST GUARDIAN
US Serial Number: 85700141
Application Filing Date: Aug. 09, 2012
Register: Principal
Mark Type: Trademark, Service Mark
Status: Abandoned because no Statement of Use or Extension Request timely filed after Notice of Allowance was issued. To view all documents in this file, click on the Trademark Document Retrieval link at the top of this page.
Status Date: Feb. 16, 2015
Publication Date: Nov. 20, 2012
Notice of Allowance Date: Jan. 15, 2013
Date Abandoned: Feb. 16, 2015

The last extension on the trademark came on July 2, 2014 from SCEA. That was their third of five allowed time extension periods. It's also important to note that Sony's previous trademark of the name (number 77750563) was also abandoned before all of their extensions had been used. What this means is anybody's guess right now. It could mean that Sony simply forgot to renew the trademark on the name. It could also mean that they did not renew on purpose and that the project is effectively dead or renamed.

The last anybody outside of Sony has seen anything from The Last Guardian was back in 2010.