The 16 years is true and the normal way to get the Swordmedalj. (20 years for officers equvalent, the Sword-order). But in some cases, usually in war, it could get quicker!
Thus there is one true story about this ensign (a von Braun I think) who did get his Sword order on the battlefield, his colonels gave him his own. Nice and well? No entirely. Because it WAS the very highest order one could get, so he was not allowed to get lesser orders after it. No orders for bravery, no orders for good shooting, nothing...
After 20 years of good service he still had only one medaljon, this Sword-order. But most of his collegues - had most of these smaller medaljs and orders, and most of them also this Sword-order too - after their 20 years of good service.... :=(
They say he was the last ensign to get this Sword-order. After him it was only captains and above who were allowed.
All in all: your grand-dad could thus get a sword-medaljon after just one excellent deed, if he was also a well merited soldier. He COULD. But this story does sounds rather fabricated...
And taking a new name wasnt THAT complicated, many did it, especielly if they had the so called patronymikon... :=)