Where it does not matter
Someone searching "waterproof dog coat size L" does not care whose shop it is. Category and problem searches are winnable from day one.
Where it does
Brand searches, obviously — and comparison queries where a known name reassures. You will convert worse there and should expect it.
What to do about it
- Compete on specifics: shipping, returns, guarantee, price.
- Real reviews on the page, yours, not borrowed.
- Accept that your blended numbers will look worse than an established competitor’s. Compare non-brand to non-brand.