My domain service provider requires at least 2 of nameservers (DNS), but I can provide 4 of them. Will that make any difference in SEO?
The reason for two or more name servers is for fault tolerance/redundancy. I've always seen at least two, one primary and a secondary name server, with possible replication to other name servers. I'm not sure, but the RFC may require a minimum of two as well.
That being said, I've never heard of the quantity of DNS servers impacting SEO. The numerous name servers your hosting company is providing is more likely driven by their own infrastructure or management purposes than SEO purposes.