This myth doesn’t exist in the actual Ramayana. He was an abuser who mocked Mahadeva out of sheer arrogance.
On seeing that Pushpaka couldn't move, surrounded by his advisers, the rakshasa began to think. "This can go wherever it wants. How has its movement been impeded? What is the reason why Pushpaka cannot advance? This must be the act of someone who is on this mountain." The intelligent Maricha spoke to Dashagriva. "O king! There must be some reason why Pushpaka cannot advance." Bhava's follower, the powerful Nandishvara arrived by his side and fearlessly addressed the Indra among the rakshasas. "O Dashagriva! Return. Shankara is sporting on this mountain. Therefore, this mountain has been made impassable for birds, serpents, yak-shas, daityas, danavas, rakshasas and all creatures." His eyes turned coppery red with rage and he descended from Pushpaka. Saying. "Who is this Shankara?" He went to the bottom of the mountain. He saw the lord Nandishvara standing not far away, holding a spear and resembling a second Shankara. The rakshasa saw that he was an odd kind of human and ignored him. In his foolishness, he laughed, like a cloud filled with water.
Mahadeva upon this punished Ravana by imprisioning him under a mountain which crushed Ravana’s arms. This led to him being named as Ranava.
'He approached the mountain and spoke these words. "O lord of the earth! This mountain has prevented my progress and has impeded Pushpaka's movement. I will destroy its foundation. O Bhava! What powers allow you to sport like a king? It should be known to me. I do not know why I should be scared." O king! Having said this. he inserted his arms under the mountain and tried to raise it, the way a predatory beast raises a tree with an animal on it. O Rama! At this. Mahadeva laughed at what he had done. As if he was sporting, he pressed down on the mountain with the big toe of his foot. Thus pressed, the hands that were under the mountain were crushed. The rak-shasa's advisers who were present were astounded. The rakshasa became angry at his hands being crushed. He emitted an extremely loud roar that filled up the three worlds. Thinking that the worlds were about to end, humans were terrified at the sound. The gods were also agitated and were distracted from their own tasks. Mahadeva, seat-ed on the summit of the mountain, was pleased. 550 Freeing his hands, he addressed Dashanana in these words. "O roamer in the night! I am pleased with your valour and your ferocity. You let out a roar in your pain and that one was extremely terrible. Therefore, your name should be Ravana and this will be your name. Gods, humans, yak-shas and others who are on the surface of this world will address you by this name-Ravana, who makes the worlds scream. 551 O Poulastya! Confidently proceed along whichever path you want to follow. O lord of the rak-shasas! I am giving you permission to leave." Ravana obtained his name from Maheshvara himself. Having greet-ed Mahadeva, he mounted the vimana. O Rama! After this, Ravana roamed around on earth. Here and there, he started to obstruct the extremely brave kshatriyas."
Simply put Ravana didn’t any songs in Mahadeva’s honour He purely got saved because of his destiny to die at the hands of Shree Rama.
This is a classic case of bully behaviour. Ravana mocked others because he believed he’s all powerful, until he got owned.
Never glorify Ravana. He wasn’t bhakt, he was a vile criminal and rightfully suffered for his crimes.