User blog comment:TheDoctor230/Barry Hasn't Defeated a Big Bad Yet (Technically)/@comment-26537965-20180110135435/@comment-24152851-20180111200836

He used to be Barry, but by his own admission "that man is dead". He underwent a loss of identity and embraced his Savitar personality. They were the same person up until the point Barry ran back and pulled him from the timeline, from there on in their histories are different.

This is a similar concept explored in Futurama, where time duplicates can be created through time travel http://theinfosphere.org/Time-paradox_duplicate. Once created they live their separate life to the original and can never be the exact same person again.