Currently they are not universally required to do so. For example character ai's characters don't[1]. Scammers use these models while perpetuating frauds.
The frontier models most of us work with (ChatGPT, Claude, Gemini, Grok, Kimi, GLM) do declare they are AI's.
Should all models be required to answer this direct question in the affirmative, overriding any other system or user prompt?
[1] I put up a quick demonstration here in case you aren't familiar:
https://imgur.com/a/srTlCZn
Yes. I would add they should have a mandatory "report" function. "Report this scammer" should trigger a review of all recent interactions the user has performed and if it looks like they are abusing the system to scam people it must escalate to a human operator at the LLM and they must click a button the bundles the interactions and uploads everything required by the national authorities of the given country and also lowers the karma of said country. If the country loses too much karma they lose access to the LLM meaning they lose revenue and businesses are impacted if they ignore their own scammers.