My Geiriadur Mawr has three different names for goldfinch - nico, eurbinc, teiliwr (telor) Llundain. But if you look the other direction (Welsh to English) you only have nico actually entered, but that entry also lists jac nico, peneuryn, and pobliw (as well as the others) before saying GOLDFINCH.
Curiously, in the English to Welsh side, there is also an entry for just finch which gives *asgell fraith, pinc" and then lists some specific types:
BACHELOR - ji-binc
GREEN - Llinos werdd, pila gwyrdd
MOUNTAIN; BRAMBLING - bronrhuddyn y mynydd
And when I looked for telor (something), all the birds listed were warblers. The more you try to follow a bird name to the other language direction, the more it gets mixed up!