AI assistants don't browse a website the way a person does. They work from a mix of sources: what they were trained on, information they retrieve live from the web while answering, and structured data and citations that describe a business clearly and consistently across the places it appears.
What tends to make an assistant confident enough to name a specific business:
Clear, machine-readable structure. Schema markup and well-organized pages spell out exactly what a business offers and where it operates, instead of leaving the AI to guess from marketing copy.
Consistency everywhere. When a business's name, services, and area served match across its own site, its listings, and other mentions of it, an assistant is far more comfortable stating that information as fact.
Content that actually answers the question. Pages written to directly answer the kinds of questions people ask, rather than pages built purely to rank, are easier for an AI to quote and easier for it to trust.
Conversely, thin, inconsistent, or contradictory information makes an assistant less likely to name a business with confidence. It will often hedge, or simply recommend a competitor whose signals are cleaner. That is a content problem more than a visual one, though a site nobody has updated in years usually has both, which is why a modern website design and clean, answerable content tend to arrive together.