Share of search is a great metric, but it certainly has it's limitations and it's not useful for all brands. Some common examples where share of search is difficult or impossible to rely on is:
One or more of the brands you compare has a wide product portfolio, covering multiple verticals
One or more of the brands is difficult to spell (e.g. Hyundai, Schwarzkopf), has variations or nicknames (Coke, Coca-Cola, Cola) or a name connected to other common words or categories (Eastern, Norwegian).
The brands or category you research is very niche and has low search volume (e.g. specialized B2B brands)