Yes there's no official breed name, even the more established crosses which have been going for generations like labradoodles haven't got 'official' kennel club recognition yet.
That's because Labradoodles are not a breed, they never can be as long as one parent is one breed and the other parent a different breed.
You can only have a 'breed' when both parents are of that breed.
Obviously back in the mists of time there will have been a cross breed eg Goldern retievers and Irish setters have a common ancester and were bread into distinct gun dogs.
This why jack Russels were around for 200 years before becoming a KC registed breed in the last decade.
OP
Your dog is a mongrel.
I get quite angry about these 'breeders' who tell people lies about their dogs. Aquaintence has a 'cockerpoo' which isn't. The 'breeder' told her cockaspoos will be a registered breed in 40 years.
She also intends to 'breed' him.
I'm working on that one.
Just about every breed has some health problems, but it seems there are fewer with dogs bread to be working dogs rather than dogs bread purely for theur looks.
OP
I'm sure you love your dog and I'm sure he is lovely, I hope he doesn't develop health issues.