Sadness is not my name

[Leanne]

Hi there! There is definite potential in this poem and you have a good ear, which is a very big part of the battle already won, but there are some issues that I'll address here -- bearing in mind that this is Serious Critique, so it's fine-toothed-comb time.

Sadness is not my name -- is this the title or the first line? I'm not a fan of it being both -- and I'd prefer it as the first line. As a title it tells too much about the poem.

Yet I was born with
A similar pain ~ under
The placenta
Came this nourishing -- the word "nourishing" is very odd in conjunction with "pain" and "fate", and not really odd in a good way Personally I would put an adjective with a negative connotation here to highlight the pain. Also, "came" is a strange verb to use as it sounds too colloquial here -- perhaps "lay" instead? That would keep your assonance intact.
fate.

Hate is the
Opinion of giants and
Monsters roaming and
Storming my head. -- three line breaks on articles/conjunctions -- this is a waste of breaks really. Try to keep in mind that when we read a poem we pay the most attention to the first and last words on a line, so we really need to make them count. There's nothing memorable about "and". I don't have an issue with breaking on these words occasionally but it must be for a reason and I can't find one here that's good enough. You might even find that this poem works better with longer lines interspersed with the shorter.

Why
Must the sky
Dawdle when we all -- the personification of sky is very nicely done
Need to need?

Bent
Over and handcuffed. -- again an issue with the line breaks -- when enjambing, the break really ought to do double duty and give words a little shift in meaning when read separately or together -- this doesn't.

The lime and the
Scum rubbing off the -- no need for "the" here
Threats, screaming and cleaving -- cleaving what? This can't be just left here on its own
That there is no one left. -- this might work better if you put a colon after whatever you change the previous line to, and take out "that" to make it a bolder statement.

Escape
Is the fate of scientists.

It is a mystery for all the rest. -- this line might benefit from a switch to "for all the rest, it is a mystery" -- not imperative but it's a preference thing