Yes you can. Well, elements of it. Your YouTube channel (in fact any form of digital communication channel such as TikTok) is part of your brand, and the more it grows, the more important it is to protect the branding elements that define what your channel is about, such as channel name, logo and any slogans or catchphrases associated with your channel.
Examples of Trade marked YouTube channels include MrBeast, JackSepticEye and Pewdiepie. You don't need to have millions of subscribers on your channel however, with the increasing monetisation opportunities on the platform (such as merchandising and sponsorships) it makes sense to protect your brand sooner rather than later.