Kyle Reese had Sarah Connor’s picture, so he knew what she looked like. The Terminator only had her name and that she lived in LA. His plan was to kill all Sarah Connors who lived in LA because that would be the only way he would be sure he’d get the right one. The Terminator only knew which Sarah Connor was his target after Kyle protected her.
So why couldn’t Kyle have gotten to her first and just convinced her to change her name (Sarah Connors kept getting murdered, it wouldn’t have been a hard sell) and run away? They wouldn’t have had to destroy the Terminator, and thus leave a part behind to be exploited by Cyberdyne Systems. It would have avoided Judgment Day.
Best deleted scene ever.