To Carry on the Family Name and Values

There are plenty of people out there who want to carry on the family name and the family values.

Of course, this tends to apply to the father's family name, but the point is that many prospective parents want to continue the historic family lineage.

They find joy in knowing that their child will bear their last name and keep the family going. Again, this is all based around societal customs.

prospective(adj) 可能成为的   

lineage (n) 家系、家族  

bear (v) 持有、带有