To answer your question: halakhically, there's no requirement to name the first issue after the deceased. In fact, according to the
Talmud "הבכור" may refer to the
brother of the deceased, not to the nephew. (In context, "name" is taken to mean inheritance.)
Yet, biblically, we do find the notion of naming the child after the deceased, in the context of yibbum - as appears from
Rashi on Genesis 38:8 (והקם זרע. הבן יקרא על שם המת:). See also Ramban and Mizrachi on the verse.
As for your suggestion, we now shortened the (somewhat-verbose) explanation in the brackets to include only an essential translation of the term yibbum.
Sincerely,
Shmuel