The situation is as follows:

One server at a location with the old site still working.

I changed the hosting and made a new site, changed the nameservers at the registry.

When I enter www.sitename.com I see the old site, but when I enter sitename.com I see the new site.

What can I do?

Problem is with the Look-up Files.
Check them

Check your CNAME and A Records for www and * or www and blank