Business Name for SEO?

I have a question about business name and how it relates to optimizing SEO. I am creating an LLC, does that name matter if I’m going to be operating the business under a different name, using a DBA? I’m buying an established business, and will be keeping that name, but I am having to create a new LLC to purchase the assets. So I wanted to make sure if I need to be strategic in selecting my LLC name, or if it is mainly the DBA name that matters for SEO (I’ll be keeping their current domain and website and be looking to optimize it going forward.)