Has "Social Media Analyst" become now a recognised job/career in the Middle East?

It might be too soon for that, as generalist social media roles are just starting to pick up.

Unfortunately I believe not.
There is a growing awareness among business owners about the importance of Social Media.
However It's almost the same person(s) responsible for a channel or several will involve on creating strategy plan, executing them, and analyzing them (in case they really analyze them)