"Dw i'n mynd i Aberteifi."
Translation:I am going to Cardigan.
Yes, you do when they are expressed differently in different languages. If you were translating a French document into English, you would change 'Londres' to 'London'. If you were translating an English document into Irish, you would change 'Galway' to 'Gaillimh'. The same applies with Welsh to English, or vice versa.
A few place names in Welsh start with the definite article, eg Y Bala
In this case the sentence is 'dw i'n mynd i'r Bala' (I'm going to Bala)
In most other cases there is no definite article in front of the name of the place, eg Aberteifi
So you don't need the 'r and the sentence is 'Dw i'n mynd i Aberteifi' (I'm going to Cardigan)
I think it wouldn't be proper English to say that I'm going to Bharat, Deutschland, or Zhongguo, because those aren't how you say those places in English. You'd say you're going to India, Germany, or China. As much as I might call this Welsh town Aberteifi first and Cardigan second, the English word for this place is indeed Cardigan.
However Duolingo decides to approach the issue, I agree that they should be consistent.