Reference: http://mufti.af.org.sa/ar/content/حكم-من-ذكر-أسم-الله-داخل-الحمام
Question: At home, we have a toilet in the same room as the place (bathroom) where we do wudhoo, so should I utter the Name of Allaah inside the bathroom when making wudhoo or not?
Response: Mention [the Name of] Allaah within yourself – without uttering it. So you [should] utter the Name of Allaah within yourself when making wudhoo, and that is sufficient in shaa.-Allaah.