My son has not seen his father for over a year. He has chose not to have any contact with our son. I am wanting to find out if I can file for his rights and to change my son's last name.

First where are you at, the laws vary.

But in general, you can't take his "rights" away, you may modify the existing child visitation order to get him no or less visits. And you can ask his permission to do a name change, and if he agrees, you just change it with him signing for it also. If he does not agree, you will have to file in court and show a reason it is in the best interest of the child. Or perhaps the bio father will not show up to fight it.

Also do you have a child support order in place, and if so, is he paying it, if you don't have a order ,why not?

We are in OR and the last time my son saw his bio-father, he was trying to kidnap him and my other son for money. I left the state of TN to protect my children. He is a known drug abuser and dealer. He has stated he is going to kill our son so he does not have to pay child support, and my son is very scared of him. I don't want him having any rights for future needs. My son was born with my last name, but in the state of TN they automatically change the child's last name when child support is going. He has not paid child support in 4 years. I have to keep my children safe.

When using a site like this its usually best to browse around a bit first to see if you can find similar threads. Had you done so, you might have found this sticky:
https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html

Based on your initial post, the answer would have been no. However, if the kidnapping attempt has been documented and you can prove the father is a danger to the child, then you may be able to do this.

I would strongly advise consulting a local Family Law attorney to advise you on this. An Attorney will know how to get this before a judge without endangering the children.