I wanted to ask if it is ok to have the name (Sawda'). Which means sort of black, and if it is ok to change it?

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.

It is not clear to us whether you meant (Sawda') or (Sawdah), anyway both of them are derived from the Arabic word 'Sawaad', which is the black colour. There is no harm in both cases to be named with any of them. On the contrary, the name of one of the mother of the believers was Sawdah.

Finally, if there is any religious benefit in changing any of these two names then there is no harm on the condition that the necessary procedures are taken to protect one's rights and not lose them due to the change of name.

Allaah Knows best.