I am not sure if there's a word for it, but if there's no word for it what's the next best way to say it, is there a short phrase or something you can think of? I am thinking of a blob of hair arranged in such a way so that it's not messy and attached with something like an elastic band or something else to make sure they don't come apart.
If you mean a sample of hair that is cut off neatly and bound together on purpose (to be a keepsake, decoration, or lab sample, etc.), I think the word is a "hank" of hair.
"In the drawer were his baby shoes and a hank of golden hair from his first haircut."
There are many words for different arrangements of hair. I can't tell from the question which one you want, but these are likely options:
If all the hair is tied in one bundle hanging down in the back, that's a ponytail.
A blob of hair that is hanging together (but probably not tied) is a lock.
Hair that is still on someone's head, and bound together for neatness or style would usually be called a "ponytail". https://en.wikipedia.org/wiki/Ponytail
Hair that has been cut off and bound together in order to be kept as a form of keepsake would be called a "lock of hair". https://en.wikipedia.org/wiki/Lock_of_hair
Hair is hair.'
Hair has strands. As in:
She had a strand of hair hanging down in her face as she washed the car.
- (Loose) strands of hair can be held in place with bobby or hair pins.
- Strands of hair can be held in place with barrettes or clips.
If two dogs or cats fight, they might rip out hunks of each other's hair.
The hair on your shower floor could be called a blob of hair (though that sort of turns the stomach).