This is a good question. I guess the answer is: no, but if you don't include any 'assisted-by' tag then you are asserting that the text or code is the fruit of your brain.

More importantly, I think the "assisted-by", or whatever tag, could contain something more useful than the name of the LLM. What tasks the LLM was used for, for example. "initial code generation" could be one, and some projects might think that's a great or a terrible idea. "checking my code after I wrote it" could be another, and even the anti-AI people might agree that that makes sense and that human-written code that is checked by an AI tool is better than human-written code that was not checked by an AI tool - or some projects might value the checking done by some tools but not others.

When I use LLMs to write a document, I sometimes keep a table with one LLM's suggetions in column 1, a second LLM's suggetions in column 2, my comments on picking or merging them in column 3 and then my own text in column 4. Maybe we should have standards and tools to document how code was written (and checked).