内定先って英語でなんて言うの？

You can simply say new company.
For example: "I will be starting at the new company next month."
Prospective employer is any employer who is considering a person for employment.
Therefore it may not only mean somewhere you will be employed but companies you have gone for interviews for.

Firstly, it is not a 'prospective employer'. A prospective employer is a possible or potential employer - for example if you have yet to attend an interview and be offered a job. The job is only a prospect, not a fact. If you 'will' be working for a company, you are no longer a prospect. You are a future employee.
You may speak in terms of the workplace, the employer or the employment.
Eg. "John future workplace is situated near London."
Eg. "John's future employment is near London."

Example
"I went to my new company today."
or
"I visited my future employer today."
or
"I am going to be working here in the future, this is my future employer."

▪Future employer.
future=likely to happen in time to come

▪Considered company
considered=believe to be

▪Soon-to-be employer
soon-to-be=planned or destined to have

"Potential employer"
" An impending employer"
"A prospective employer"
"Potential employer and impending employer" can be used as alternate terms to describe a person who has received a job offer and will be joining the new company in the near future. "A prospective employer" means any employee who is considered for employment. "Prospective candidate can be used to explain future employee.

A place of work that a person has accepted an offer of employment from could best be described as their 'new job'.