Dam lines

Dam lines are frequently used to name females, e.g. Olde House Caroline 8th. However, it seems to me that unless such founding dams have frequently been bred to sires of similar breeding, then the genetic significance, at least the nuclear DNA of the founding dam in the line, is progressively reduced with each generation. However I understand that the mitochondrial DNA within the unfertilised cell, which has important function, no doubt amongst other things, in respiration (powerhouse of the cell), is inherited from the dam (I see this absolute position disputed), although this varies in species but apparently female ancestry in cattle can be studied through the relatively unchanged passing down of mtDNA from mother to her offspring. One would like to know whether the eggs formed in the female, early on in her life, indeed during embryonic developement, are contributed to by her sire only with respect to half of the half set of nuclear DNA in the unfertilised ovum, or if her sire also contributes to other ovum features, like the cell wall, the cytoplasm, etc. The question boils down to, what do geneticists like Dr. Matthew Hegarty, who provides services to HHBI, or anyone that views this blog, have to say about the importance of dam lines in one's breeding programme in the genetic context?