Informal:
* Purse
* Handbag
* Clutch
* Bag
* Tote
* Satchel
Slangy:
* Pocketbook (can be considered old-fashioned, but still used)
* Clutch bag
* Shoulder bag
* Shopping bag
* Kit (British slang)
More playful:
* My little black book
* My money bag
* My essentials carrier
* My secret stash
The best slang term depends on the context and the desired tone.
For example, "clutch bag" is more fashionable than "shopping bag," while "kit" is a more playful term.