VB.Net Properties - Public Get, Private Set

Yes, quite straight forward:

Private _name As String

Public Property Name() As String
    Get
        Return _name
    End Get
    Private Set(ByVal value As String)
        _name = value
    End Set
End Property

    Public Property Name() As String
        Get
            Return _name
        End Get
        Private Set(ByVal value As String)
            _name = value
        End Set
   End Property

I'm not sure what the minimum required version of Visual Studio is, but in VS2015 you can use

Public ReadOnly Property Name As String

It is read-only for public access but can be privately modified using _Name

One additional tweak worth mentioning: I'm not sure if this is a .NET 4.0 or Visual Studio 2010 feature, but if you're using both you don't need to declare the value parameter for the setter/mutator block of code:

Private _name As String

Public Property Name() As String
    Get
        Return _name
    End Get
    Private Set
        _name = value
    End Set
End Property