Rivers get named as people far more often than mountains or seas do, and in the Indo-European world a striking number of them are named as women.
Comparative mythologists reconstruct a river-goddess whose name survives in Sanskrit Dānu and, apparently, in a whole cluster of European river names — the Danube, the Don, the Dnieper and the Dniester among them. The reconstruction is not universally accepted in every detail, but the cluster is hard to explain any other way. Sanskrit Sarasvatī names both a river and a goddess, and she outlived the river: the watercourse itself is thought to have dried up in antiquity while the goddess became the patron of learning and music.
The vocabulary is more fragmented than for most concepts here. Indo-European had at least two words for water — one giving Latin aqua, the other giving Greek hýdōr, Russian voda and English water — and river words are frequently local, because rivers are.
What recurs across quite unrelated traditions is the association of rivers with speech, music and continuity: something that keeps moving and keeps sounding. A good number of the names on this page are as much about that as about water.