What is lower pin called that holds front hub assembly to suspension arm on 96 lasabre

The ball joint connects the hub assembly to the lower control arm ("A" arm). The pin you are referring to is likely the ball joint stud. It's best to use a tool like the one below to separate the ball joint from the control arm:

http://www.harborfreight.com/cpi/ctaf/displayitem.taf?itemnumber=99849