meaning of - rite - at the companies names
Solution 1:
When native speakers see "Rite Company," said Company would like the patron to think "Right," as in "correct" or "accurate," or maybe even "righteous."
There are no solemn ceremonies at Rite Aid or Shop Rite that would pass for a rite.
Dictionary.com defines rite as:
a formal or ceremonial act or procedure prescribed or customary in religious or other solemn use: rites of baptism; sacrificial rites.
(Although signing the disclosures for your prescription may be a formal act or procedure, there is no religious component.)