The correct technical name for a single spark of a firework is a "star". Each star is a small roughly spherical pellet made mainly of gunpowder.
A fuse ignites a lifting charge and a time-delay fuse. Whilst the lifting charge burns, it propels the firework into the air, then near to the peak of its trajectory the time-delay fuse ignites a bursting charge packed behind the stars. This bursting charge both ignites and distributes the stars. Chemical additives in the stars determine their burn colour. They are called stars both before and after ignition.
You can find many labelled diagrams of the inner workings of fireworks if you search online for "anatomy of a firework" or similar. Here is one example:
You may call them streaks.
Google search for "firework streak"
3 a : a narrow band of light
streak [in American]
2. a ray of light or a flash, as of lightning
Webster’s New World College Dictionary, 4th Edition. Copyright © 2010 by Houghton Mifflin Harcourt. All rights reserved.
to grow to such length as to droop over toward the ground
to move, flow, or extend slowly in thin streams
something that in shape, appearance, or position is like an animal's tail
Example (as more than the head is circled):
Palm Tree – An aerial effect that produces a gold or silver stem as the shell rises into the sky (known as a rising tail), followed by a brocade or willow effect that creates palm fronds. It resembles a gold or silver palm tree in the sky.1
a fire or blaze of light used especially to signal, illuminate, or attract attention
A pellet of composition which is propelled from a mortar or shell and produces a long tailed effect
In addition to the provided answers, I would refer to it as an offshoot.
- A side shoot or branch on a plant.
1.1. A thing that develops from something else.
‘commercial offshoots of universities’
In this case, I consider it related to 1.1 (more literal than its example showcases), because it is a fragment of the initial explosion.