Q:

Who Am I? (A Dead Guy)

You seek him who died at sea,
Try and find who he might be.
A heart that did not wilt in flame,
Writ on Roman stone is his name.
Nothing of him that doth fade,
But doth suffer a sea-change,
Into something rich and strange.
Now with his Adonis he lies,
Who thought not himself worthy of fame,
And writ on stone not his name,
That lies beneath lit and unlit skies.
Who am I?

A:

I am...

 Percy Shelley, the early Romantic poet.

You seek him who died at sea,
Try and find who he might be.

 Shelley drowned when his boat sank.

A heart that did not wilt in flame,

 Legend has it that Trelawny plucked the heart from Shelley’s funeral pyre to be buried with his son.

Writ on Roman stone is his name.

 Shelley is buried in Rome

Nothing of him that doth fade,
But doth suffer a sea-change,
Into something rich and strange.

 These lines from The Tempest are written on his grave.

Now with his Adonis he lies,

 This could have a few meanings: Shelley died with a copy of Keats’s poetry in his pocket, and his poem Adonaïs is written in Keats’s honour.  His heart is said to have been kept inside his widow’s manuscript of Adonaïs.  His ashes were later found in an envelope inside his daughter-in-law’s copy of Adonaïs.  He was also buried in the same cemetery as Keats.

Who thought not himself worthy of fame,
And writ on stone not his name,

 Keats himself requested to be buried with no name or date on his tombstone.

That lies beneath lit and unlit skies.
I don’t know what this refers to.

