I was wondering if there is a musical term for this particular ornament/embellishment, whereby a singer (or instrument) suddenly glides up an octave at the end of a note.

For example, this oldies song by Jo Ann Campbell is loaded with them: https://www.youtube.com/watch?v=jBUcj7ed0wU

and first occurs on "mama" at 0:22, "out" at 0:27, "mama" at 0:44, "go" at 0:50, and "rolling" at 1:00.

Perhaps it's some kind of yodel or hiccup? 
 
Just curious.

Glissando, a musical slide.
 
Jo Ann is definitely glissing, but there's also melisma, but that's more for stretching a syllable over a series of pitches. Billy Joel singing Allentown springs to mind for some bizarre reason.
 
In current music, melismas definitely rule. Glissandos, like Jo Ann's, hark back to grand opera traditions (even grander than the "Grand Ole Opry").
 
Although, now that I type it, I'm realizing that auto-tune is bringing glissandos BACK. All these pop tune choruses suddenly scooping up 8va (or 15va, yikes). Hah, what goes around comes around.
 

we trombone players call it a glissando

Ok, thanks.  Glissando it is.