In other breeds Dapple is referred to as Merle, but it is the same just named differently for the Dachshund, not sure why.
Your're exactly right, the only way to have a dapple pup is one of the parents
must be dapple! They're no health risks associated with a single dapple. As was stated it depends where on the body the dapple shows itself. If it has blue eyes (one or both) then it MUST be a dapple even if dapple colors are missing from the rest of the dog. But it does not have to have blue eye(s). Genetics notation would be Mm for a single dapple dog, MM for a double dapple, and mm for not dappled.
Double Dapple is where the problem lies. If 2 dogs that are Dapple (Mm & Mm) are allowed to mate and the dapple gene is passed from
both parents (not all pups have to be dapple remember) then you end up with a double dapple (MM). They generally have more white on them then normal but not always. If the gene that is passed from both parents ends up hitting the same spot, specifically the eye, then the dog could be born without eyes, distorted eyes, blind etc. There is also a chance of the dog being deaf. The chance of health issues is not worth the risk.
A double dapple and a piebald/dapple can look very similar because of the amount of white on the dog. If you look at our website you'll see our little girl
Chloe is a Smooth Blue Tan Dapple Piebald. NOT A DOUBLE DAPPLE.
Our current mother
Lucy is a hidden (or cryptic, as stated above) dapple, she as an adult does not show any dappling but did as a pup and the spots faded. She produces Dapple pups, but to look at her she is a Red Brindle. One of her parents was a dapple, therefore she could have been a dapple, if either one of her parents were not dappled. Then I would have explored the father
Casey's side. His parents were not dappled.
A way to check for the possibility of a double dapple pup is to look at the pedigree. If both parents are listed as being dappled then there is a chance that the pup could be a double dapple (see above), even then it does not guarantee a genetic defect. Remember both parents must pass the dapple gene to the pup and of that passing both must effect the exact same spot, in this case the eye(s) Not all breeders list the dapple on the pedigree so there is not a guarantee unless they listed both parents as being dapple. Lucy for example was registered as a RED. Now that I know 100% sure that she is a dapple because she threw dapple pups I'm going to change her pedigree. Registration services like
AKC and others will allow you to change the dogs color but not the name.
I hope the additional information was of some help,