so I changed my apple ids name. I downloaded a movie in 2011 with the previous name. My computer was reset and I don't have the movie anymore. can I re-download it on iTunes because I bought it once? if so how?

Whether you can redownload the film for free depends upon what country that you are (it's not possible in all countries), whether you've changed countries since buying it, if the studio allows redownloading, and if the film si still in your country's store - what you can redownload will show under the Purchased link under Quicklinks on the right-hand side of the iTunes store homepage on your Mac's iTunes

And on your iOS devices via the Purchased tabs in the store apps.