Populate data on another sheet based on dropdown criteria from the first sheet

I would like to be able to populate the corresponding box on sheet 2, based on the box criteria that is selected from the dropdown on sheet 1. In essence, if the box changes on sheet 1, it would automatically place the name in the new box on sheet 2. Also, is there a way to format it so that the names are placed in short columns within the box, rather than one long column? This seems like it should be straightforward, but I am not having any success with VLOOKUP or MATCH. Any help would be greatly appreciated. Sample worksheet is attached.

DILIPandey,

Thanks for your excellent solution! I'm wondering if you can review a variation of what I submittted to see why it isn't working for me. To further refine where the names populate based on their Box # and Corp. Title, and then placing the name in the correct grid, I have tried adding an AND statement to your original IF statement. My updated formula is in cell B3(purple) of the attached sheet (Potential Grid Sample-original). Your formula is in cell B4 (red). I think I am close, but must have a syntax error. Any additional insight you can provide would be most helpful. Thanks again for your solution.

Formula:

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Fantastic. I will have to study how the formula works without the use of an AND statement, but I appreciate your expertise. Thanks again.