As a historical question, we rarely know the names of the composers of individual prayers. Some parts are taken directly from the Hebrew Bible, others were composed in the first centuries of the Common Era, others were introduced in the Middle Ages and up to modern times. So the Siddur is really an anthology of prayers that expressed the spiritual needs of Jews in different times and places. In the modern period we are more aware of people who compose particular prayers and in our Siddur, unless a name is directly attached, the author can usually be found in the 'Sources of Unnamed Prayers, Meditations and Reflections' on page 744.