For example, if I don't get Veronica as a companion, will she still have an ending slide?

No.

In my first game I did not get Gannon or Raul. No slide.

I didn't get ending slides for some of the companions I did get (I got them all).

I got Cass's, Raul's, ED-E's, Lily's, and Rex's. Veronica (my most used companion), Boone, and Arcade were no-shows.

Mine gave me some story about what Boone went on to do, even though I killed him.

I got all the endings except Boone's. It was saying in the end lily left me and all that crap but it never happened... I killed lily so the ending is as generic as the story, sad and a big disappointment from FO3