Cloud's Heaven's Cloud has some interesting history in Japanese culture, read the following excerpt from Japanese Swordsmanship: Technique and Practice by Gordon Warner and Donn F. Draeger:

"The greatest and most revered of Japanese swords is the Ama no Murakumo no Tsurugi (Gathering-Clouds-of-Heaven Sword), alternately called Kusa-nagi no Tsurugi (Grass-mowing Sword)."

It is basically one of the three sacred regalia of the imperial family, and without all of them, the family can not take the throne.

"...The sword is a straight-bladed, double-cutting-edged type with a perfect balance. It denotes courage..."

A remarkably similar description to Cloud's Heaven's Cloud.