"Ceri Lingo and Dewi Lingo's mouse is brown."
Translation:Mae llygoden Ceri Lingo a Dewi Lingo yn frown.
A noun followed by a proper noun is definite by default.
llygoden Ceri = the mouse of Ceri / Ceri's mouse.
You can't add another y(r) to it.
Because that would be "The mouse" whereas the English statement is contains no definite article.