I am not sure if this is what you are looking for. But if you are using Visual Studio, right click the Shared project, select Properties, click Resources, select Strings, Add Resource, Access Modifier: Public, give the string a name and value. Then you can use the string in your code:
I have just been able to try your suggestion. When I add a shared project I can't access the project property page. (And I couldn't find a way to access) So I can't add the resource file. But I had tried adding resource files directly to the Radzen project instead of another project. It's working conceptionally. In this case, the resources are being acceable. But when Radzen recreates the codes the files are gone. The ignore list can be used in this case but I couldn't succeed in that. I asked that to the team. This question can be read from here.
If the project is shared, you need to add the Shared project to the server project as a Dependency. Then, if the Resource has a Public Modifier, you should be able to access the string using the syntax below: <Solution>.<Project>.Properties.Rescources.<ResourceName>
If that is not working for you, I would need to have access to your solution to diagnose the issue.
As far as Radzen removing the Resource files, if the solution that Atanas provided does not solve the issue, I am uncertain of a better solution.
Your suggestion and @korchev's method (can check out from this page) are working together seamlessly (If the resource key used directly to the label, for example, Radzen design window shows [Expression] instead of the real word (or key). If you need the follow the resource keys on the screen you can create page properties and can use them.).
I changed a little your suggestion. In my scenario, I do not need a shared project. I'd added the resource files directly to the same project. I'd added the resx files in the Pages folder to the ignore list. Radzen doesn't create new resx files anymore for the new pages. The following syntax is enough to use resource keys. Properties.Resources.<ResourceKey>
Because the resources are already in the same project.
I suggest this method to all Radzen users if they want to create a multilanguage / multicultural application.