No, it is not allowed to do so. The Hadeeth says: Allah curses any one who enters in a family who is not his, and any one who leaves his family. لعن الله الداخل في النسب ولعن الله الخارج من النسب.
Your family name is not just a personal consideration in your heart but it is a matter which should be known to people who know you or deal with you.
Every one was created by Allah within a family which is like the tree and we are its branches. It is a matter of destiny and decision of Allah. The person who tries to cut the branch away from the tree, will be cursed as Allah cursed in Quran those who cut ties with their relatives. Sura Muhammad, Verses 22 and 23.
Omitting your family name is not an act which Allah The Almighty wants from you. On the contrary, we need to do every thing possible to strengthen the relations with our family members who are been created by Allah as branches of our family tree.