Passing user first and last names from external db to WordPress user first and last names using session variables?

Passing user first and last names from external db to WordPress user first
and last names using session variables?

This may be a little convoluted, but here it goes. I don't let users
register on WordPress to access my member site. I have an outside
registration/login system set up and want to continue using that for new
user registration and login to the member side.
I use WordPress shortcode planted in various areas of my own HTML and it's
working wonderfully. A drawback I've noticed is that plugins (WP-Polls to
be specific) can log votes by IP, Cookie and/or Username. I want to use
the log votes and collect the user's username and archive what users have
voted for. I began the process of importing my user db table into WP and
passed the data in through the proper column headers and it all worked
fine.
Now, I want to use the user's First and Last name (which is in the user's
session) from when they logged in and pass it to the WP variable WP-Polls
uses to log users' names. My brain is pretty much scrambled and I am not
concentrating enough to figure this out.
Can someone offer some help? My PHP level is low intermediate, so please
explain it for someone who's just a couple levels above idiot. I'd greatly
appreciate it.