How can whitelabel functionality affect the page rank of a website?

Question

Search Engine Optimization

Hello, I have the following task. Need to develop whitelabel functionality for the website. There will be several domains that will lead to the same web server, where the engine is located, which will form the site depending on the address from which it was visited. So, the question is, how much can this affect the page rank of these websites? Will Google treat these sites with less trust and rank them differently? Or does the search engine not care how many websites are on one server?