Basically, several level-based games "back in the day" had a special kind of enemy appearing when playing the same level for too long. Bubble bubble had Baron von Blubba:
Snow Brothers had a similar one (a weird pumpkin figure spawning invincible ghosts).
Does this kind of enemy have a canonical name? (Like "boss", but it's not a boss of course.)
No, there is no canonical name for them.
However, I somewhat like the term Chase Boss this GiantBomb user has come up with, although it does not strictly limit the term to enemies appearing due to time constraints: http://www.giantbomb.com/baron-von-blubba/3005-10958/forums/the-mentop-tento-ten-best-chase-bosses-504317/
It's also worth noting that 1980 arcade game Berzerk probably featured the first enemy of this kind, fittingly named Evil Otto.
I usually hear this referred to as the Soft Timer (I realize the enemy itself is not a timer, but this is still what people call it).
"Soft Timer" is opposed to a "Hard Timer", which causes you to lose immediately when it runs out.
Examples:
I don't think they have a collective name, but I like to name them Arcade Enrage.
The name comes from World of Warcraft when battling a boss for too long. The boss would then enrage, increasing damage by a lot, and death is inevitable.
Somewhat the same goes for those characters.
it functions more like Baron von Blubba of the Bubble Bobble series, who operates as an invincible (but avoidable) enforcer of the stage time limit, so yes :)