Another person with a similar name was Edward Alleyne, the Elizabethan actor manager who founded Dulwich College.
As this poem by Ben Jonson shows the name was pronounced Allen (Alan), however it was written:
To Edward Allen (Alleyne)
by Ben Jonson
IF Rome so great, and in her wisest age,
Fear'd not to boast the glories of her stage,
As skilful ROSCIUS, and grave ∆SOPE, men,
Yet crown'd with honors, as with riches, then ;
Who had no lesse a trumpet of their name,
Than Cicero, whose every breath was fame :
How can so great example dye in me,
That ALLEN, I should pause to publish thee ?
Who both their graces in thy selfe hast more
Out-stript, than they did all that went before :
And present worth in all dost so contract,
As others speak, but only thou dost act.
Weare this renowne. 'Tis just, that who did give
So many Poets life, by one should live.
Anne's name was also written "Bolleyn" sometimes (eg the Holbein drawing of her). So I still think her name was pronounced Boollen (as in Woollen), and spelt in various ways.