All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
You are not obliged to change your surname because it does not include a forbidden meaning in itself. It is known that sometimes the meaning of the surname does not apply to the person; there are many people whose surnames are An-Najjaar (carpenter) or Al-Haddaad (blacksmith) while they do not work in these professions; this is indeed a general custom among people.
In addition to this, changing the surname, if it does not include a forbidden meaning in itself, such as being enslaved to other than Allah, may lead to unpleasant consequences. Indeed, changing the first name of the person is much easier in its rulings than changing his surname.
Allah knows best.