The name Shahlaei comes from the Shahlaei family (Persian: شهلایی) which was one of the powerful of the region; they were big landlords and senior officials under the Qajar and Pahlavi dynasties.
References
^Hajjiabad-e Shahlai can be found at GEOnet Names Server, at this link, by opening the Advanced Search box, entering "-3802223" in the "Unique Feature Id" form, and clicking on "Search Database".