You could potentially use a name that shares a similar meaning, if the meaning of "Janice" is important to you. However, the meaning of "Janice" itself is debated and isn't consistently defined.
Therefore, simply transliterating it (writing it with Greek letters according to their pronunciation in English) wouldn't be culturally appropriate. It would be like writing "Janice" using Cyrillic letters for a Russian equivalent; it's technically possible, but not how names are adopted into a language.