The DNA itself is not "anonymous", but I would do it without giving my real name, address, etc. They could know who the DNA is related to, but not gain more information than that.
Even better would be to swap identity with someone else who wants to get sequenced...
They know who X and Y are, and also know the identity of their son (you), so that gains them your unique DNA sequence, identified as yours specifically.
How do you plan to do it anonymously, considering what you now know?:
1. There are already multiple database containing both your parents, you, and a linkage between you and them indicating parentage. So, prior knowledge: Alice and Bob are parents of Charlie.
2. If Charlie's parents have taken a DNA test, there already exists a database linking their DNA to their name. So, prior knowledge: Alice's DNA belongs to Alice, Bob's DNA belongs to Bob.
3. If Charlie takes a DNA test totally anonymously and perfectly untraceably, it will still show up as, child of Alice and Bob's DNA. So, knowledge now includes: Charlie's (anonymous) DNA is the son of Alice and Bob's DNA
4. From these pieces of information, it is trivial to de-anonymize Charlie's DNA, linking it to Charlie's identity: the only person it could belong to is the son of Alice and Bob, and the son of Alice and Bob is already known from point 1.
Even better would be to swap identity with someone else who wants to get sequenced...