EDIT: To answer my own question, it appears not. Swedish text here says in English:
Sofus is a small black animal that accompanies Moomin and helps and to some extent imitates him in some of Tove Jansson's episodes of the series, something that is reflected in his English name Shadow, which means "shadow". In the first episode, it is Sofu's cousin who has this role, but the cousin then does not have time to be in the series anymore and hands over to Sofus at the beginning of the second episode. The name of Sofu's cousin is never mentioned in the series