You appear to have some species of
Codium, a green, desirable, hardy macroalgae with a spongy texture and may grow branches or in lumps depending on the species. It grows incredibly slowly and invertebrates enjoy grazing on its occasionally fuzzy surface since it attract edible particles (though the algae itself is highly inedible). It is commonly known as “Dead man’s fingers,” “Green fleece algae,” “Finger algae,” and “Oyster thief,” and is said not to tolerate temperates above 78° Fahrenheit.
https://www.marineplantbook.com/marinebookcodium.htm
https://www.livealgae.co.uk/green-macroalgae-species/marine-macroalgae-codium
https://www.lareefs.com/products/codium-lucasii-metallic-blue-and-green-macrolgae-1
By the way, where did you obtain that live rock?