Renaming of O365 groups

Can someone clear up some questing I have on naming groups? We want to roll out Office 35 Groups in our organization but need to define our Governance in how these are named and found in our GAL, etc. There are a few fields that seem to define a group name but the PowerShell documentation isn't specifically clear on what difference there is between a "name" "identity" "displayName" and "alias". We also need a prefix to be appended to the name for the GAL but I don't want that Prefix to show up in Outlook or OWA on the group list for users. Where exactly do these group names show up and how can I best plan to use these parameters in Powershell when creating the groups. Too many options are not exposed in the GUI to make group creation in the enterprise worth doing at this time.