Crossbred dogs and designer dogs are often referred to as F1, F2, or F3, or even F1b or F2b.
It is just the accepted nomenclature in which we can distinguish hybrid dog breeds between the different generations. This naming standard in here applies for dogs, designer dog breeds, hybrids, and mixes, but it is also commonly (and scientifically) applied to cats, cattle, plants, and most living organisms (even cells.)
P Generation
100% Purebred Dog
These dogs are the fruits of true breeding, meaning they are purebreds and belong to a specific dog breed.
Example: a Labrador, a Poodle, etc.

F1 Generation
50% Purebred-A
50% Purebred-B
These dogs are the result of the breeding of two purebred dogs. Half of each dog is the mother’s breed, and the other half is the father’s breed.
Example: a Labradoodle whose mother is a purebred Labrador and father a purebred Poodle.

F1b Generation
75% Purebred-A
25% Purebred-B
These are F1 backcrossed dogs. They result from the mating of an F1 parent and a P parent. This is used to intensify traits found in the P parent’s breed.
Example: a Labradoodle whose mother is a Labradoodle and father a Poodle.

F2 Generation
50% Purebred-A
50% Purebred-B
F2 dogs are the offsets resulting from the mating of two F1 hybrids.
Example: a Labradoodle whose mother is a Labradoodle F1 and father a Labradoodle F1.

F2b Generation
75% Purebred-A
25% Purebred-B
These are second-generation backcrossed dogs. Each F2b dog is the offset of an F1 parent and an F1 backcrossed (F1b) parent.
Example: a Labradoodle whose mother is a Labradoodle F1 and father a Labradoodle F1b.

F3 Generation
50% Purebred-A
50% Purebred-B
Offsets coming from the mating of two F2 hybrid parents.
Example: a Labradoodle whose mother is a Labradoodle F2 and father a Labradoodle F2.

Multi Generation
An F3 or higher-generation hybrid dog crossed with an F3 or higher-generation hybrid dog. This is a more generic nomenclature and is mostly expressed using the generation of each parent, such as F4 Labradoodle x F2 Cockapoo.
Example: a Labradoodle whose mother is a Labradoodle F3 and father a Labradoodle F5.