the torah says the mitzvah of yibum is for the name of the dead brother. If this is so why is the mitzvah only on the first biyah? Also, as we see that shelo kidarka, you are also yozai the mitzvah?
The Torah commands that the Mitzvah of Yibum be performed (Devarim 25:5). That is the Mitzvah. The Gemara requires that in order for there to be an obligation of Yibum, both parties involved must be able to have children (TOSFOS 20a, DH Yavo). The Torah does not require, as part of the Mitzvah, that a child be produced. In fact, the Gemara explains the verse discussing the son which is born from the Yibum union (Devarim 25:6) not to be discussing the child at all, but to be discussing other laws of Yibum, such as which brother is obligated to perform Yibum (see Yevamos 24a).