No need to call. Just book through your favorite website/online (Expedia, Kayak, Travelocity . . ). It is not a big deal - once you have done it a few times. It is the first time that tends to feel fraught with “I might be doing this wrong.” But you are not. Watch some YouTube videos (search: travel with cello). They help a lot.
(And yes to “Violincello Yourlastname”)