"personal wish" is correct and usable in written English.
You can use it to refer to an individual's expressed desire or ambition. For example, "My personal wish is to one day publish a book of my own stories."
"He's absolutely at the top of my personal wish list," Makhathini told me.
Although you may be disappointed, my personal wish is that you find fulfilment studying at another fine college".
Neither made the cut on the day of, but both are at the top of this editor's personal wish list.
This proposal dovetailed with Lincoln's personal hatred of slavery and his "oft-expressed personal wish that all men everywhere could be free".
"It's my personal wish that the process will be increasingly tolerant as Chinese society and the economy develops, to allow creative people more and more space".
My personal wish list includes a photo album ($78 to $95) covered in thick, colorful Icelandic wool or a matching cachepot ($74) for my desk (lime green, please).
Just before the last general election, May set out her own personal "wish-list" to reform counter-extremism strategy.
"Everybody's home seems to be a kind of personal wish-fulfilment," Elsa Lanchester remarked of Hollywood's penchant for whimsy and hyperbole.
With warm personal wishes, Sophia".
The other note indicated "personal wishes".
Sacrifice personal wishes, he recited, that all may be free.
