If it makes you feel better, if you become a pharmacist and go to the UK you might be best known as a chemist:
1 British - A shop where medicinal drugs are dispensed and sold, and in
which toiletries and other medical goods can be purchased:
‘antihistamine tablets are freely available in chemists’
1.1 A person authorized to dispense medicinal drugs.
2 A person engaged in chemical research or experiments: ‘chemists have
developed catalysts that can turn low-grade fuels into petrol’
As it is, I'd be a bit concerned that simply saying you are a chemist would be misrepresenting yourself, in that being part of a profession generally means you are employed (or have been employed and continue to keep up your affiliation). It is more an in-context, implied matter of what is assumed in natural conversation, rather than a hard and fast rule.
One problem is that in a natural environment if you say you are a chemist, a person would commonly ask something like "where do you work" or "how long have you been a chemist" - to which you would need to back-peddle and explain that your undergraduate degree is in chemistry, but you are not and have not been employed as a chemist.
Such a situation would make it look like you are mostly "blowing smoke" and trying to make yourself to be something you are not. If you simply said, "my undergraduate degree is in chemistry", and optionally, "and I'm studying to be a pharmacist", that makes the situation clear and there can be no mistake about it.
As a comparison, if someone said they were a philosopher and it turns out they just have an undergrad degree in philosophy, I'd squint disapprovingly at them for being full of it. In some professions this would be much worse - for example, I will have a degree in psychology, but in very few situations would it ever be permissible to say that I'm a psychologist, as that happens to be a special title reserved for licensed clinicians.
It's all about clarity - and honesty - in your communication. Saying something that is technically true, but gives a false impression, should be left to slimeball-salesman types and politicians.