New Company Name & Branding - Same Location As Old One & Old One Exists - How to compete?

Hey folks,

So I built a website for a farm. They sell Truffles and breed dogs. It's the same land as the farm that their parents started in 1999. Their parents have a website for their dogs, and the truffles.

Their parents still want their own websites and keep it running as if it's their business, and their kids who now mostly run the farm want their own website that I made, and it's re-branded under their own name.

I'm noticing the website isn't ranking at all for the dog puppy keywords, and the truffles are nowhere to be found. I'm using RankMath with Wordpress.

I did just open this website a week ago, I know it takes a while for search engines to crawl. I will publish some blog posts etc.

I guess my question is:

Are the search engines penalizing the new branded website for using the same address, much of the same content and same products being sold as their parents websites, with a higher authority?

Any ideas on what would help?

Thanks.