resolving host names from parallels (windows) to Mac (mavericks)

Question

I was given a macbook for work that is running mavericks. We also do windows development. I'm currently running windows 8.1. I set up mysql on the mac side that both the windows 8.1 running on Parallels and the macbook need access to. I set up the users appropriately so my Parallels machine could access the Mysql db by using the computer name of my Mac (comp-123) as the mysql host address on the Windows machine. This was all working and maybe an update screwed something up. Not sure. But I can no longer access comp-123 from mysql. I try pinging that machine name from windows and it doesn't work. I try pinging the ip address of the mac and it works. I also can set the ip address for the mysql host address instead of the host name and that works. So my questions are:

1) does the ip address ever change? home network vs work network? i don't want to be hosed by manually typing in the ip address every time when computer name seemed to work so well up until now.

2) is there a better way to solve my problem or make the host name correctly resolve to the ip address somehow by editing some hosts file somewhere? I'm on a VPN connection to my work so I thought that everything would work like I was at work.

Thanks in advance.