In everyday speech, 眼睛 (yǎnjing) is much more common than 眼 alone. 眼 by itself appears more in written Chinese and compound words: 眼泪 (tears), 眼光 (vision/insight), 眼前 (before one's eyes).
Left 目 (eye) - the indexing radical. Compresses to a tall narrow form on the left side. 眼 is the everyday word for 'eye' (modern colloquial), while 目 is its more literary cousin. The radical pulls 眼 in alongside 看 (look), 睛 (eyeball), 睡 (sleep).
Right 艮 supplies the sound (gěn → yǎn, an irregular but established alternation, also seen in 限 xiàn). Faint semantic echo: a fixed gaze. Same phonetic family: 根 gēn (root), 跟 gēn (heel), 很 hěn (very) - all on 艮.
