Changing last name when getting married

[Amra94]

The verse says (Free-minds translation): "But if you do not know their fathers, then, as your brothers in the system and your patrons", ç

so mother´s name would be the last option, even in the mother is always known but the father is not for sure (only the mother can know, and it depends on the case)  the law might enclose the presumption of paternity but reality is other thing.

Then it follows: "There is no sin upon you for what mistake you made by it; but you will be responsible for what your hearts deliberately intend. God is Forgiver, Merciful".

How can someone deliberately intend something by naming (call) a child? 

But their hearts did intend to make that child their child by giving it their family's name. Except if it's just for legal purposes or something like that.