Even though Skype is technically just a video chat platform, I'm pretty sure copyright to what you broadcast would default to you. If you want to make it clear, I'd watermark (c) maya77 or whatever. Technically that's not quite right unless maya77 is a registered LLC, but at least the intent is crystal clear. DMCA is a law, the Digital Millennium Copyright Act, which requires that sites take down content on receipt of a notice by the copyright owner or their agent. DMCA.com one of many companies offering services as an agent. That logo is part of their shtick and nothing to do with the law. You have the right to have content taken down regardless of logo.
Note also that you should not include your legal name or address in any DMCA notices you might file for yourself. The content of the notice is not considered copyrighted or confidential, and many companies (e.g. Google) publish the notices after they act on them.