I recently changed my company name and moved all of my files from my old server to a new server. All of the files are exactly the same, I just moved them all to a new server when I changed my company name. I redirected all of my files that are still on my old server to the new site, using 301.
I was preparing to submit my new website to search engines but was wondering...since my old site is currently in the search engines, should I submit my new site that has the same exact files (same text, data, etc) as the old site, or would that product duplicate content at this time? Should I go ahead and submit the new site (domain) or should I give the search engines time to realize that my old site has been redirected to the new one? Or since my old site is still alive (just redirected) do I even need to submit my new site?