Hall had published in early 1598:

The earliest surviving title page naming Shakespeare (Shake-speare, just to be accurate) was the quarto of RICHARD II from 1598. Every surviving quarto before that was anonymous. Only "Venus and Adonis" and "The Rape of Lucrece," by the time of Hall's satire, had been printed with Shakespeare as the author. It would make sense then that Marston would identify Labeo as Shakespeare by reference to one of the only two works in print noting the person who actually was published as the author of these poems. And it wouldn't make sense that Marston would out Shakespeare as the non-author of plays as yet not published in Shakespeare's name.

But does that mean either Hall or Marston denied Shakespeare authorship of only "Venus and Adonis"? Of only the two poems in print at that time attributed to Shakespeare? Of more? Why not more? What in Hall's broad satire suggests that Shakespeare's authorship of "Venus and Adonis" is singularly denied?

Perhaps somewhat carelessly on my part, I took your assertion that Hall doubted Shakespeare's authorship of Venus & Adonis, and that Marston repeated these doubts, at face value.

More fool me. :)

In 1597, Joseph Hall wrote, or published, the first edition of Virgidemiarum, claiming to be the first English satirist.

In 1598, Marston wrote, or published, The Metamorphosis of Pigmalion's Image and Certaine Satyres, heavily influenced by Ovid, and also Juvenal. 

There is a poem - I think it's the postscript - which has the lines:

"So Labeo did complain his love was stone,

Obdurate, flinty, so relentless none".

In the same year, Marston also wrote, or published, The Scourge Of Villanie, in which he attacked Hall, apparently angered by the claim he'd made in Virgidemiarum of being the first English satirist.

Both The Metamorphosis of Pigmalion's Image and Certaine Satyres and The Scourge Of Villanie were published under the pseudonym W Kinsayder.

In 1598, Hall released a further edition of Virgidemiarum, with a further edition then following in 1599: Virgidemiarum - The three last bookes. Of byting Satyres.

I believe it's in these last that Hall makes his jibe about ""For shame write better Labeo, or write none/Or better write, or Labeo write alone".

So Hall's jibe about fake names is nothing to do with Shakespeare but about Marston/Kinsayer, and the poem being criticised isn't Venus and Adonis, but The Metamorphosis of Pigmalion's Image and Certaine Satyres.

So the "evidence" of contemporary doubts about Shakespeare's authorship  - isn't.

You claimed you had more - do you?

Mark Haslett wrote: To help his readers Hall identifies his purpose: to call out another poet for criticism. He says Labeo will not admit that Hall’s criticisms hurt him because Labeo writes under a pseudonym.

SB replied: Yes, Hall attacked Marston, who published under the pseudonym W Kinsayder.

Mark Haslett wrote: So here, in plain print and using a direct quote, is a contemporary of Shakespeare's named Joseph Hall declaring in print that the author of Venus & Adonis uses a pen name.

SB replied: No, Hall is declaring that Marston used a pseudonym.

Mark Haslett wrote: But no men, women or children anywhere under any circumstance wrote a word about Stratford Will being a writer of any kind until long after he died.

SB replied: In 1598, Francis Mere's Palladis Tamia (1598) praised Shakespeare as a writer, while The Parnassus Plays of around 1599-1601 mocked his pretensions of being one.

In 1605, William Camden described Shakespeare as "most pregnant witts of these ages our times, whom succeeding ages may justly admire".

In 1607, Sir George Buc, Master of the Revels, positively identified Shakespeare as the author of King Lear.

And let's not forget the royal patent of 1603 naming Shakespeare, alongside Burbage, Heminges and Condell as being part of The King's Men, and Heminges and Condell in 1623 affirming that he was the author of the plays in the First Folio.

Mark Haslett wrote: Seems pretty straight-forward.

SB replied: Indeed. I don't know why anyone would have any reasonable grounds for doubting Shakespeare's authorship.

SB replied: Or maybe Marston's poems were circulated before being published in a volume, as was pretty much standard?

Mark Haslett wrote: But then, how would Hall expect any of his readers to identify "Labeo" as Marston when no one has ever heard of Marston?

SB replied: Were[ the lines  ""For shame write better Labeo, or write none/Or better write, or Labeo write alone". published in the 1597 edition of  Virgidemiarum?

This isn't a snide question - I'm having problems tracking down an online copy that I can read.

Mark Haslett wrote: Please provide a direct quote where Francis Meres says Shakespeare is a writer from Stratford or where the Parnassus plays do the same.

SB replied: Meres attributes eight plays to William Shakespeare. All eight appear in the First Folio, whose publication has been arranged by John Heminges and Henry Condell, who knew, and were named in the will of, William Shakespeare who died in Stratford-Upon-Avon.

The Parnassus Plays scorn Shakespeare's lack of learning - which they would hardly do if he was actually Oxford.

Can you provide a direct quote from any of Shakespeare's contemporaries in which they directly state that he wasn't the author? You promised to do so in an earlier post, but I haven't seen anything further.