The bifurcation happened in the second half of the 19th century when the Ūla, due to its channel erosion, crossed the water divide between its own and the Kotra's drainage basins.

As a result, the Ūla enlarged its basin by some 410 square kilometres (160 sq mi) and the Kotra lost two of its tributaries.

Simas Karaliūnas suggested a Slavic borrowing in Lithuanian katãryti/katãlyti (from Russian: колотить, колотать) 'to beat, to whip' as a possible source of the name.

Edward Bogusławski presented Kotra as a Finno-Ugric name (without further elaborating it; Rimvydas Kunskas suggested Finnish: *kaatarha 'to flood (kaataa) a backgarden (tarha)').

Šarūnas Šimkus suggests the name may come from a pronoun Lithuanian: katrà, katarà, Russian: котора(я), Ukrainian: котра 'which [of both]' (fem.)