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Yes this is a good idea. I like the 4-character versions the best.
I would go for names like Vector3. It is the best for both beginners and experts. In linear algebra these are also called vectors, not "V2's".
No I definitely think "V3" is too short. But I'm worried about line-length for complex types. Maybe using the regular GLSL names is a nice idea.
End of the day, I don't really mind which way it goes.