How do I know if the LLMs trust my service?

That is the honest starting point and it is worth sitting with, because the alternative on offer is a number somebody invented. OpenAI, Anthropic and Perplexity document their crawlers and their robots.txt tokens. None of them document what makes an assistant recommend one supplier over another.

What you can observe is what they say. Ask each assistant to recommend someone in your category, in your city, for your kind of work. Do it without naming yourself. Whether you appear, who appears in your place, and what it says about them is a description of your standing that no dashboard will give you.

Then ask directly about you by name. There are three answers and they mean different things. It describes you accurately, which means the corroborating material is out there and consistent. It describes you vaguely or wrongly, which means the material exists and disagrees with itself. It has never heard of you, which is a different problem with a different fix.

The second case is the common one and it is the most fixable. Models reconcile what they find. If your title is different on LinkedIn than on your site, if your company name appears three ways, if a directory has a five year old description of you, the model is accurately reporting an inconsistent record. Making those agree is unglamorous and it works.

Beyond that, the observable pattern is that corroboration carries the weight. Being described by sources that are themselves widely cited does more than anything you can write about yourself. That comes out of testing, and observation is all I am claiming for it.