These are several flowers in one stalk. I have them in yellow, purple, red, pruple - white blooming right now. Very very beautiful!! Does these have a name?
Gladiolus :-D what pretty colors they are. Your instincts are good, they are in the Iridaceae (Iris) family of plants, though they are not what are commonly called Iris.
Please post more Gladiolus-photos! I have to start mine indoors in April, plant them outside at the end of May and pull the bulbs up once the first night frost has been. It's too much work, so I'd rather admire yours.