Electrical tape, heat shrink tubing, duct tape, friction tape, rubber cement, or nothing at all. Heat shrink tubing can be bought at most auto parts stores and 3/4 is probably what you want for that particular cordage. If you have any of those other things at your house already though, use that instead.
If you want to protect it, you already got good recommendations. I just wanted to add that Teufelberger ships all of their eye to eyes like that, so I wouldn't worry about it. I think the hitch cord will be worn out long before the stitching.
Or, more rope-y/knotty, you could bind the sewn part with mason line or 30#? fishline (something that comes to about the same thickness, i.e.) as a seizing --could be a series of several multiple(-wraps) Strangle knots.
Ah, here's a (dark) photo of some end whippings with multi-strangles + sailmaker's whipping finish.
In these, I put in an extra buried x-ing of the whipping ends --there's usually just one--; this influenced the length, finding that for mason line about 5 overwraps works and in that monofilament it was 7-8. A more traditional sort of seizing/whipping could do as well. (depends on how much fun you find it!)