I'm still kind of a beginner with learning the guitar and just wanted the community's opinion about pentatonic shape/pattern names. I've come across several different ways the 5 boxes are named. The way that I've been taught is shape one (in A minor) starts at the 5th fret, shape 2 the 8th, shape 3 the 10th, shape 4 open, and shape 5 at the 3rd. Other youtube videos refer to them in a different order. I guess my question is: Is there a standard that when you say pentatonic pattern 1= a specific shape...?
I think you partly answered your own question. Due to different order given throughout Internet, I think you'd better to keep the system you get used to. But I can be wrong.
They don't really have names, because the shapes themselves don't really mean anything - in the greater scheme of things they're not particularly important. The notes the scale contains, the sounds its made up of - those are the important things. For example, the A minor pentatonic scale is composed of the notes A C D E G. It doesn't matter how you produce those notes, a guitar, a piano, a trombone, a kazoo...if you play those notes it's the A minor pentatonic scale. The shapes are just a quirk of the instrument you happen to play, the guitar. Now the guitar differs a bit to most instruments in that the exact same note can appear in multiple places, and that means any scale can be played in several ways, hence the multitude of shapes.

However the important thing to understand is that all those shapes are just made up of 5 notes - A C D E G. If you learn the notes on your fretboard learning and understanding scales will become a lot easier.
Actually called Mark!

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whataboutbob The unsual way of naming these is by where the root(s) of the pentatonic fall in the shape.

E.g, for A m pentatonic:

Shape 1 (aka region 1): rooted on (6,5), (4,7) and (1,5) (string, fret)
shape 2: rooted on (4,7) and (2, 10)
shape 3: rooted on (2, 10) and (5,12)
shape 4: rooted on (5, 12) and (3, 14)
shape 5: rooted on (3,14), (6,17) and (1,17) [and (3,2), (6,5), (1,5)