Many in our family have at least 2 middle names. Especially in the older generations they are named in a particular sequence. In other words the eldest are named after the grandparents; while the following ones are named after aunts and uncles of either side (in specific order). My father for example, his middle names are a reference to an uncle and aunt. Based on the name of his aunt, it could also serve as a reference to the Virgin Mary.
In my generation, at least among my cousins and siblings, I predominantly see references to the grandparents. For example I am named after both my grandmothers. But I also see brothers being named after their grandfathers, but using different parts of the grandfathers names.