Macbook Air External Monitor Resolution Asus VS248

I just bought a new Macbook Air for personal use (OS X El Capitan 10.11, early 2015). I have the same Macbook Air for work (OS X Yosemite 10.10.5, early 2014).

• My work Macbook Air connects to my Asus VS248 external monitor perfectly. In Display arrangement, both screen resolution are set to "Default for display".
• PROBLEM: My new Macbook Air, while using the same cables, has very poor resolution on my external monitor when using "Default for display". I've tried scaling the resolution, but the highest resolution is 1920x1080 and for some reason when I select this setting my external monitor is off-center and doesn't use about 1-2 inches of the screen on the left.

THEORY: On my work computer that has no issues, the external monitor is Display setting window is recognized by model number VS248. However, on my new computer that's having issues, the display settings does not say VS248. Rather, it simply says "Display" and my computer is "Built-n Display". My theory is that my work computer is recognizing the model number for some reason, and because it's recognized I have no problems with "default for display" setting. Because my new computer doesn't recognize VS248, it may not receive the defaults, which is why "default for display" doesn't work on my new computer.

Does this sound plausible? If so, how can I get my new computer to recognize the model number of my Asus monitor? Is this a OS difference between El Capitan and Yosemite?

Thanks,