Is it okay for a girl to have a surname of Dai and a name of Yuan?

Yes.

The meaning of the name "Yuan" refers to nobility, power, solidity and down-to-earthness, and it means auspiciousness and connotation.

The original meaning of Yuan is wall. In ancient times, cities or government offices would have courtyard walls, so it was extended to be a city or a code name for some government offices. Walls are used to divide a certain range. Therefore, in traditional astronomical terminology, "wall" also refers to the defined range of constellations. Taiwei, Ziwei, and Tianshi in the middle palace are specifically called the three walls. (Solemn statement: The answer content is for reference only, please do not be blindly superstitious).