I have a question about my choice of name for publication. I recently got married and legally changed my name to my husband's surname (for example's sake: from Hunter to Jones). So, despite legally being Ms Jones now, I would quite like to use the hyphenated name Hunter-Jones in the professional context and in publications. This is so that people realise that it is still me and so that I can somewhat keep my maiden name. Is this possible or do I have to use my legal name professionally and when publishing? Thank you for any help
Yes. You get to decide what name appears on your publications.
In the same tune as @Ric: The best is to keep one name for all of your publications. If you introduced a middle name (like Jane Abigail Doe), keep the pattern, too; and not change once to Jane A. Doe and an other time to J. Abigail Doe, for example.
In addition, consider a free registration at Thomson Reuters's Web of Science as ResearcherID (here) or -- better and -- ORCID. By this you may increase the visibility of your research activities, not only should your name be a more frequently one (Smith, Li, etc.); but should you change to an other research institution. See, for example, the ResearchID bag by John Kitchin below: This allows everyone to see the bibliographic references he contributed: this compilation is accessible, regardless if one has subscriber access to Web of Science, or not. Obviously, ORCID has a database that lives from your contributions.
Disclaimer: I am not affiliated with Thomson Reuters, nor ORCID. And while not affiliated with Kitchin's group either, it is simply historically the first page of a PI I saw with this badge, while researching for his contributions to Emacs' org-mode.
I know a number of people who, although they legally changed their name upon marriage, continue to publish under their maiden name. I consider that a valid choice.
You can use any name you like, but consider your goal. Many professionals continue to use their maiden name, if it is established. Consider it your 'business name'.
Legally and morally there is no issue. Whether changing your name is wise depends on your subject and the databases used in that subject. For example, in mathematics publishing under different names would be no problem, as MathReviews has a database of authors both identifying name changes and different spellings and differentiating between different authors with the same name. In other subject areas changing your name means that users of a database will not find all your publications. This will even be true for the change from Hunter to Hunter-Jones, as many computers will not see any relation between the two. So think about the databases used most often in your area, and search for people who changed their name.