As far as I know he was given name Dashanan because he cut his head 10 times and offered to Lord Shiva to please lord. So there are so many version of it. I think his real name was Ravan and Dashanan was given name by Shiva.
But Dashanan means "one having ten heads". Even before Ravan worshipped Lord Shiva, Ravan had ten heads. This means that he was known as Dashanan even before he worshipped Shiva. Moreover, he did not offer his ten heads to Siva but to Brahma.
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