If you are wanting to host these videos on your own website...
1.) Purchase everything (domain + hosting) using bitcoin or a pre-paid card that you bought with cash
2.) Purchase everything with a new/fresh email
3.) Purchase the domain using fake info (you can use fakenamegenerator)
4.) For more obfuscation you can purchase Whois Protection with your domain
5.) Put the website behind Cloudflare and patch up any methods that could be used to find your website's IP (use google)
6.) If you will be streaming extremely questionable/distasteful videos, then you can go for offshore bulletproof hosting
7.) Do ALL of these steps while you are connected to a secure VPN that keeps zero logs
I am not sure if this is overkill for what you are asking. If you are simply wanting to keep your video viewers from getting your info, then just utilize steps # 2, 3, 4, 5. If you are attempting to hide from everyone including government officials, then utilize all of the steps above.
Hope this helps OP.
Edited by Optimiztix, 24 January 2016 - 06:07 PM.