Can you use brand names in search arbitrage ads and keywords?
With great care, and often not at all. Using a company's name or logo in an advert so that people think you are that company is misleading and may infringe its trade mark. Traffic platforms and feed providers restrict branded creatives and keywords, and brand owners complain quickly. Generic category terms are safer and usually perform more predictably.
Trademark policy varies by platform and country, but the common thread is confusion. An advert headed with a retailer's name that leads to a page of search ads implies an affiliation that does not exist. That is a misleading ad under platform rules and potentially under consumer law.
Branded search terms are a related problem. A visitor who clicks a "Brand X login" suggestion and lands on ads is the classic navigational query being intercepted; the advertiser ends up paying for a customer it already had. Many providers block branded forced keywords for this reason. The same logic is why typosquatting on brand misspellings attracts legal action.