Asking for a Working From Home option or your own personal office seems like something you should negotiate in advance.
For Work From Home, try to ask only if your job is possible from home and negotiate on a certain salary politely keeping the WFH condition on the table and providing a reasonable explanation of the same. It’s good to convey this as a suggestion.
For Office Space, if your work requires concentration, you can politely ask for a private space to work, and provide the benefits it would have for the employer(I’ll get more done for the company!)