LowercaseControllerModelConvention.cs

public class LowercaseControllerModelConvention : IControllerModelConvention
{
    public void Apply(ControllerModel controller)
    {
        controller.ControllerName = controller.ControllerName.ToLower();
        foreach (var action in controller.Actions)
        {
            action.ActionName = action.ActionName.ToLower();
        }
    }
}

Usage.cs

services.AddMvc(options =>
{
    options.Conventions.Add(new LowercaseControllerModelConvention());
}