If my name was Mo-Nercy Son of Flame, I would probably want to pass that on as well.

You look at your kids and see yourself.....your spouse, your mother and father, your spouse's mother and father all bundled into one or in my case two or however many kids you have.
You see that and it reminds you....of the very best of your family....and if they are gone......deceased.......it enables you to hold on to that very best....

Anyway..my two cents worth on the issue.
That is all well and good but gives a reason to have children rather than a cultural obsession to "pass on your line" by having children. I understand the point of having kids, but I do not understand the reasons people give to go out of their way to make sure their family name lives on.