No. There is a sample form available, but it is not a prescribed form. It is perfectly fine to sign a Living Will using a different form or even no form at all.
There are, however, specific rules for how a Living Will must be signed and witnessed. A valid Living Will must be signed in the presence of at least one witness or a notary public. The Health Care Agent is not an authorized witness, nor is anyone involved with providing health care to the signer.