All AGPL / GPL licensed code requires that the AGPL / GPL license also be distributed with the application. Moreover, AGPL / GPL also requires public attribution (acknowledgement / credit) of those who have created and contributed to the source code.

Ofcourse, if somebody wants to be dishonest and unethical, they can violate these terms to hide the fact that they are using AGPL code in their SaaS application. There's not much you can do about it in such cases. But if anyone (like current or former employee) leaks this info to the public, they can face legal trouble and bad PR in the future as it would be akin to using pirated software.

In general, you don't, but that's a different question.