Did you require it? Your question is really confusing, modules run in the environment they are required, so a module required by a localscript runs in a localscript environment and follows the rules that localscripts follow, otherwise if by a server script, then it follows the rules server scripts follow. If you avoid _G you will save yourself from some headaches. Why do you need _G anyway.
I never seen a professional developer uses this, I think it’s useless because it literally replaces ModuleScripts. I believe it’s deprecated and might cause errors.
Since the server is requiring it (client can’t require by ID) then you are using it in the context of the server, therefore client can’t get _G.Name. This is exactly why I am discouraging _G – use modules that are shared between the server and client (which you want) in a folder in ReplicatedStorage and require that on the client.
Do you need to require by ID though? I think this can be solved by just making it a module in replicated storage, so both server and client can see it, and your issue would be solved (and would also eliminate the need of _G)