I installed Ubuntu on my machine and decided to have all my gaming needs on Ubuntu. I installed Steam using WINE for my Windows games however this is mostly not possible for my other games. I could install the other games using the Windows Steam client but I doubt that they would run well because they're newer games so I'd like to be able to play them using the Linux Steam client. When you install a Steam client on a new computer it logs your machines hostname so wouldn't that cause a problem with me wanting to have a Windows and Linux Steam client on one machine? Thanks!
I have run Steam on Linux and Steam on Wine on the same system. (At the same time as well.)
Your machine's hostname is mostly another bit of data they collect, it's not something that particularly matters since you can set it to anything. Steam is not particularly restrictive in that regard - you can be simultaneously logged in on multiple systems, but some (most?) games can be played only on one system at a time (though it's usually fine to have them installed on multiple systems at the same time). It's best to keep the library folders for the two separate though.
Whether the games you want to play are available for Linux is a different problem.