The act of rinsing is 漱口 (to rinse the mouth); adding 水 (water/liquid) makes it into 'mouthwash.' In ads you'll often see 含漱液 as a pharma-marketing variant.
memory
漱 (rinse mouth) + 口 (mouth) + 水 (liquid) - 'mouth-rinsing liquid.' The character 漱 has 氵 (water) on the left, signaling its water-related meaning.
