Valentinian theology sources (some) describe the "Elect" as possessing the "Name". It seems this notion of possessing the "Name" comes from the Book of Revelation where it is said to be written on their foreheads (Revelation 14:1 cf. also 22:4)?Indeed the Gnostics in general (that is various Gnostic groups) were concerned about possessing the Name. This wasn't because of Revelation exegesis though. In fact, Revelation displays an interest in this same phenomenon, as do many other Christian sources. Name possession was part of Christian ritual.
And now my question(s)...... What does possessing the "Name" mean in Gnostic tradition..... and does this particular Gnostic notion have a following in our time?
The Name that the Christians were wanting to possess is the Name of God, the divine unutterable Name, usually written as the tetragrammaton YHWH. The Christians understood that Jesus possessed this Name, that it was given to him when he was exalted to heaven. It is this Name that they are baptised into and likely it is this Name they are writing on their heads when they were anointing their converts with oil.
The Name was powerful. It did more than identify them as God's. Possessing the Name meant that they possessed the power of the Named, and were transformed by that power. It transfigured their souls. In addition, possession of the Name guaranteed them entry into God's realm at death. It is the password that let them into heaven. Think of it like the ticket you need to get into the VIP box at a sport's game. If you have the ticket, you can pass into the box. Otherwise you are turned away.
The Gnostics made the Name their trade secret so that different groups claimed that they knew the "real" Name of God and its pronunciation. If you joined the lodge, they would teach it to you. The Ophians used Kaukalkau. The Valentinians used IAO. Marcus the Valentinian used Jesus Christ, although he claimed that the name had a secret aeonic pronunciation known only to the aeons and revealed to him in a vision. The conventional Christians used a formula like "in the Name of the Father, the Son, and the Holy Spirit." Or some used "Jesus Christ." Although the conventional Christians understood this to be the YHWH Name given to Jesus.
This is still practiced in conventional Christianity. After water baptism, the convert is anointed with oil in the Name. As for what modern gnostic groups do or don't do ritually, I haven't a clue.