Why should the name of our father be withdrawn from among his family because he had no son? Give us a holding among our father’s brothers.
Torah Temimah: Sifrei
English: It was taught: R. Yehudah says, “name” is said here and “name” is said there [in yibbum] “he shall rise upon the name of his brother” — just as there it means seed, so here it means seed.
Gezeirah shavah on “shem.”
Preserving the father’s “name” is about continuing his line through inheritance.