Yo hablo con la cuando yo necesito una habitación en el hotel.

Recepcionista is a feminine singular noun. Recall that a noun is a word or group of words that is the name of a person, a place, a thing, or activity or a quality or idea. Since this is a feminine singular noun, then the matching definite article is la, which is feminine singular, too, as indicated in the sentence. On the other hand, recepcionista means receptionist. Finally:

Yo hablo con la recepcionista cuando yo necesito una habitación en el hotel.

yes you are correct