LTE is called "Long Term Evolution" because it represents the next step (4G) in a progression from GSM, a 2G standard, to UMTS, the 3G technologies based upon GSM. Calling it LTE has no relation with speed but if you say calling it 4G then yes.
In the initial days it was called as 3.9G (because it was not meeting the expected bandwidth of 4G) but for marketing reason companies started calling it 4G to have marketing edge and same is true for HSPA+ which is 3G technology.