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Is this what you need?
<https://www.pulumi.com/docs/reference/pkg/dotnet/Pulumi/Pulumi.DeploymentInstance.html#Pulumi_DeploymentInstance_StackName>

that looks like it! is there an example code?

You could look through <https://github.com/pulumi/examples> for any repos with `-cs-` in their name.. I couldn't find any examples of DeploymentInstance in use.

In case anyone is wondering, the property is         var stack = Deployment.Instance.StackName;