Since you have the luxury of a double surname, there is an easy solution that avoids having to go back and correct older publications: use Leyli Jafari from now on. Spanish authors do this all the time, they have a double surname but typically only use the first in their scientific publications (one of my Iranian students also decided to drop his second surname to simplify his citation record).
Databases (Web of Science, Google Scholar) will be able to connect your older publications with author name "Leyli Jafari Taghvasani" to your new publications "Leyli Jafari" (in particular if you have a unique ORCID identifier), and colleagues who type "Leyli Jafari" in a search engine will be directed to both sets of papers.
I checked on Google Scholar that there is no other "L. Jafari", so dropping the second surname should not complicate matter in that respect (and I notice you are already following that practice here on Mathoverflow...).
But the main benefit of the ellipsis is that you will not have to explain this embarassing story that your advisor changed your name...