If we care about preserving a "self" and we also believe that someone is still the same person when on drugs or when their hormones are playing up (this is not intended to be sexist, although I suppose it could sound like that) or when they are just really angry, then we shouldn't be too worries about brain chemistry.
There are new possibilities here for personal growth in ways that have not been possible before.
I agree. For a very positive spin on transhumanist brain chemistry engineering, I recommend reading http://biopsychiatry.com/
We usually don't worry about personality changes because they're typically quite limited. Completely replacing brain biochemistry would be a change on a completely different scale.
And people occasionally do worry about these changes even now, especially if they're permanent, and if/when they occur in others. Some divorces are made because the partner of a person "does not see the same man/woman she/he fell in love with".
The naïve way of understanding mind uploading is "we take the connectome of a brain, including synaptic connection weights and characters, and emulate it in a computer". However, people want their personalities to be uploaded, not just brains. That is more than just replicating the functionality of their brains in silico.
This nuance has lead to some misunderstandings, for example, to experts wondering [1] why on Earth would anyone think that brain-centredness [2] (the idea that brains are "sufficient" in some vague sense) is a necessary prerequisite for successful whole brain emulation. Of course, brain-centredness is not required for brain uploading to be technically successful; the problem is whether it is sufficient for mind uploading in the sense that people actually care about?
The first obvious extension that may be required is the chemical environment of the brain. Here are some examples:
Whole Brain Emulation - A Roadmap includes a short section about the "Body chemical environment" and concludes that for "WBE, the body chemistry model, while involved, would be relatively simple", unless protein interactions have to be modelled.
The technical aspect notwithstanding, what are the practical and moral implications? I think that here's not only a problem, but also an opportunity. Why keep the accidental chemistry we have developed in our lifetimes, one that presumably has little relation to what we would really like to be - if we could? Imagine that it is possible to create carefully improved and tailored versions of the neurotransmitter "soup" in the brain. There are new possibilities here for personal growth in ways that have not been possible before. These ways are completely orthogonal to the intelligence enhancement opportunities commonly associated with uploading.
The question of personal identity is more difficult, and there appears to be a grey zone here. A fictional example of the protagonist in Planescape: Torment comes into mind - is he the same person in each of his incarnations?
The second extension required to upload our personalities in the fullest sense might be the peripheral nervous system. Most of us think it's the brain that's responsible for emotions, but this is a simplified picture. Here are some hints why:
In short, different chemistry in the brain changes what we are, as does the peripheral nervous system. To upload someone in the fullest sense, his/her chemistry and PNS also have to be uploaded.
[1] Randal Koene on whole brain emulation
[2] Anders Sandberg, Nick Bostrom, Future of Humanity Institute, Whole Brain Emulation - A Roadmap.
[3] Bradley Voytek's (Ph.D. neuroscience) Quora answer to Will human consciousness ever be transferrable?
[4] Selective serotonin reuptake inhibitors
[5] Bear et al. Neuroscience: Exploring the Brain, 3rd edition. Page 564.
[6] Michael W. Eysenck - Perspectives On Psychology - Page 100 - Google Books Result
[7] Endoscopic thoracic sympathectomy
[8] Enteric nervous system
[9] Scientific American, 2010. Think Twice: How the Gut's "Second Brain" Influences Mood and Well-Being
[10] The Guardian, 2012. Microbes manipulate your mind