I have a few.
- Squin "feels like victory"
I like that one, sounds like a memorable brand name, while also being a unique word. the name combines "squirt" and "win", since hand sanitizer usually comes from little push-squirt bottles, and are victorious over germs.
- Protect-SAN "Shields your skin, where you need it most"
Easy to understand, has a pun, and focus's on the protective aspect of the product, which is the most important part.
- Coat n' Go "Squirt, rub and GO!"
Focuses on ease of use, and having a descriptive, to the point name. could also use a literal coat in the logo or marketing as a further visual metaphore for how it protects you.
Hope these help. :)