Do the enemy that appear in arcade game when running out of time have a canonical name?

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:

• Here and here various users call the ghost in Spelunky the soft timer
• Here some users refer to the Rebel Fleet in FTL as the soft timer
• Here someone refers fire spreading during the Butcher in Diablo 3 as a soft timer