In America a woman is custom to taking her husband's last name but islamically is she allowed to do so?
Also I have changed my name once already to be left alone from my crazy family so technically I am not even giving up a family name but rather just a name I adopted.
Mostly am I allowed to lie to my future kids about thier family name if I do not chnage to my husband's name when we get married?
I simply do not wish to contact or have my family contact me or my children in this lifetime , so is it permissable to lie to my kids about my heritage and my family name?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

We have already clarified in Fatwa 89932 that it is prohibited for the wife to take the name of her husband's family. Also, changing your family name is not permissible even if you have not taken the name of your husband's family. It is not permissible for a Muslim to attribute paternity to other than his/her father. Indeed, cutting relations with your family means severing kinship ties that Allaah The Almighty ordered to be maintained. Furthermore, this would encourage your children to sever their kinship ties. For further information about virtue of maintaining kinship ties and warning against severing them, see Fataawa 84358 and 88129.

On the other hand, it is not permissible for you under any circumstances to lie to your children regarding your lineage and the name of your family.

We alert you that dutifulness to one's parents and maintaining their kinship ties are obligatory on the Muslim, whether the parents are Muslims or not. Allaah The Almighty says (what means): {But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in [this] world with appropriate kindness}[Quran 31:15] This Quranic verse did not differentiate between the Muslim and non-Muslim parents.

However, the scholars differed about other relatives, but the preponderant opinion is that it is obligatory to maintain kinship ties with relatives of the first degree like brothers and sisters, or relatives of the second degree like cousins, nephews, paternal uncles and aunts and maternal uncles and aunts. It is preferable for the Muslim to maintain kinship ties with the rest of his relatives in general as long as he does not fear that it would entail harm. Maintaining kinship ties is a good chance for the Muslim to invite his relatives to goodness.