How do I determine battery manufacturers/companies whose batteries that have met UL 1642 certification?
If the item claims certification to a UL standard they should have a UL listed file number printed on the item, (or a number from another accredited test lab, for e.g. ETL, CSA, that actually did the certification) .  If the item cannot include printing, such as very small items, then there might be separate literature with the certification information.  These file numbers can be searched on the UL web site, (or other testing lab sites).  

Manufacturers sometimes post their certificates on there own web site, but to be sure always verify they are listed directly on the legitimate test lab site. 

Here is the page for UL: 
https://www.ul.com/database 

Here is a pdf guide to searching UL: https://fcia.org/articles/ULQuickGuide.pdf