Accessing Network Share from Machine

My coworker and I are attempting to setup a two node "cluster" in which each node needs to access a file on the first node. To make this simple (it's a dev environment), he created a network share in which the entire X drive on the first machine is shared (Everyone > All Rights). So, ultimately, I can get to the file by accessing \\xxx.xxx.xxx.xxx\X\filename.txt.

What's interesting, though, is that, while I can access the first machine from itself by using the IP address, or localhost, I cannot access it by using the name I gave it (which I resolve using the hosts file on both machines). \\my.machine.name\X\filename.txt gives me a login dialog (which I can't login with using the local account OR a domain account). However, the other machine can use \\my.machine.name\X\filename.txt and it can access the share fine. It's very confusing, and I haven't been able to figure out what's causing it.

Both boxes are Windows 2012. The account I am using is a local account (on both machines - same account name). The IPs are static. Both machines are running inside VMWare's vCloud and are in the same vapp. Any insight or even a good way to debug this would be much appreciated.