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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
There is no harm in changing your last name if it has a bad meaning and causes an embarrassment for you, Inshaa' Allaah. Changing your last name could even be desirable. It is confirmed that the Prophet changed the names of some particular people as they had a bad meaning or had too much praise. Changing the last name because it has a bad meaning does not mean being traced to other than the father. The Prophet changed the name of the tribe of Az-Zinyah (i.e. fornicators) to the tribe of Ar-Rishda (i.e. guided). Therefore, there is no harm in changing the last name.
Finally, it should be noted that you should avoid losing the rights that you have on people or the rights that people have on you, by authenticating this change in an official institution and announcing this in the mass media.
Allaah knows best.