For all intents and purposes, Shinra is meant to be just a name (in this case, the family name of the founder). And although there's no value in looking at the name's individual components, here's a quick explanation.
神 shin: gods, divine (also secondary connotations of mind and soul)
ç¾… ra: gauze, thin silk or net. Usually connotations of fine clothing, or being trapped or held back.
Quite a number of names ending in "-ra" use that particular kanji, so there's no real wonder where they could've found the inspiration; just slap "godly" onto it, makes it sound all eerie and powerful. As an interesting note, "Shinra" (æ–°ç¾…, same second character again) is an alternate pronounciation of an ancient Korean kingdom called "Shiragi" in Japanese.
The character probably also has older meanings that I'm not aware of, and also many phonetic uses, explaining its use in the very various situations it's used in (clothes, buddhist divinities, intimate bodyparts, gate names, not to mention as a writing for the pronounciation of "Latin")