The earliest archaeological evidence of the use of the star, for Jews, dates only to the 3-4th century CE, and it shares a shape smiler to that of the believed Seal of Solomon. It was believed to have give protective powers, since it represented the number 7 with its 6 points and center (3 on each triangle giving 3+1+3 a mathematical system also seen on the menorah). The earliest use of the term Shield of David comes from the 11th century and it could easily be called the Shield of David with people relating it to David instead of Solomon (which arabs/muslims related it to) and its mystical 'protective' powers (thus th shield).
If anything the double D is a more modern invention now that we can see what ancient alphabets looked like, even the dead sea scrolls had Hebrew much more resembling the modern letters than the 'very ancient' form of Hebrew (Paleo-Hebrew) which was almost exactly like the Phoenician alphabet rather than the one we now call Hebrew. Its like how a backronym works.