I have been working on the major scale and have been using the CAGED system. I understand that there are 5 common shapes but do they have a common name? That is, is each shape given a name that identifies each accordingly that is commonly understood by all?

Any help would be appreciated.

It's just "the major scale" - you identify it by the notes it contains and it's pattern of intervals. You can also look for familiar shapes within the scale pattern, the best things to use arguably are the chords that relate to that scale.
Actually called Mark!

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