Not quite sure what part you're referring to... the という towards the end? If so, then yes you're right. The いう in という is really the verb 言う (usually written in kana when it's used grammatically like this) which is normally pronounced as ゆう in that form. If you try to say いう fast it just sounds like ゆう anyway. Regardless, it's usually romanized as "iu" not "yu"

言う can be a tricky word since it can be pronounced slightly differently based on a speaker's dialect. In the standard Tokyo dialect 言って would be pronounced as いって but in a Kansai dialect it might sound more like ゆって or ゆうって.