After finishing a PhD, your title is either Dr or PhD. What is the correct title while still working on it? Is it MSc?
This question asks almost the same question, but doesn't specifically ask for titles.
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You don't really have a title, per se, other than whatever other social titles already apply to you: Mr., Ms. ...
You can add MSc following your name if you have earned that, but it isn't really a title.
But you are a student.
Once you pass certain milestones, you might be called something like a degree candidate but that isn't a title. Titles (other than hereditary titles) require earning some achievement that you haven't yet earned.
Some people might want to use "Master" after earning a MSc, but that is also often used for, say, five year old boys. Probably not what you are after.
To add to the (very good) previous answers, I think it is also important to mention that the way PhD students are considered is also country dependent.
In the US, people working towards a PhD degree are mostly considered as students. They are often referred to as "PhD candidates" or "grad students" (depending on their level of advancement). The curriculum is longer (and can be started without a prior Master degree, which is usually not the case in European countries), and requires to take several classes and exams. The stipend is usually not fantastic, while the graduation ceremony is quite a big deal. Briefly, working towards a PhD in the US can be compared to getting any other academic diploma.
In Europe, people working towards a PhD degree are mostly considered as professional researchers. For instance, in France, it is common to refer to a PhD student as "scientist" or "researcher" (even though they are students registered at a higher education institution). It is not always required to take classes - and if it is, the requirement is often to simply validate a few credits once for all. The graduation process is pretty casual, if existent at all. If I were to summarize my PhD in Switzerland: I have been working in a lab doing science for some time, and at the end they gave me a piece of paper saying that I was now legally allowed to add the letters "PhD" in front of my name on my mailbox and my driving license.
I am less knowledgeable about this process in other continents. And these are only general trends, as sharp country-specific differences may exist.
The UK seems closer to the US than to "Europe" in these matters.
Here your title normally goes in front of your name, and does not change based on receipt of a masters degree, whether or not you subsequently start a PhD. You can start using the title Dr after completing a PhD, but many people don't use it, or only use it in a relevant professional context. You technically can put letters after your name following the award of any degree (including bachelors) and various other degree-like achievements, but this is never actually done in everyday life. A case where it would be done is if someone in medical, legal or related professions had a name-plate outside their place of work of the form "Jane Smith BVSc MRCVS" to demonstrate their qualifications.
Historically, however, there was a potential change in title. If Mr Paul Jones was awarded a masters degree, he could then be styled "Paul Jones, Esq.". Note that by "historically" I mean over 100 years ago, so at the time only men were allowed to get degrees. The title Esq. (for Esquire) is not really used any more and most people aren't aware that it signifies anything in particular, except that the user is somewhat pretentious. Maybe the best known recent usage is Bill S. Preston, Esq., who does not have a masters degree.
Within the Humanities in the United States, it's common to say "doctoral student" when enrolled in a PhD program, but if one has not yet advanced to candidacy. After passing qualifying exams, submitting an approved dissertation proposal, and/or whatever paperwork is required by one's university to be ABD ("All But Degree"), then one can say that they are a "doctoral candidate."