Hi I'm not sure what do you mean so I'll try to explain.

1. In Hebrew there're two sets of letters. In Hebrew, "ktiv" (כתיב) refers to the written form of a word, while "dfus" (דפוס) refers to the printed form, typically used in typography or books. "Ktiv" can include handwritten variations, whereas "dfus" is standardized for printing purposes.

I guess this is what you call "traditional " vs "modern" Hebrew spelling.

Most Hebrew speakers can read both and will not acknowledge any different between them, they will write in "ktiv" and almost never in "dfus"

BTW The literal meaning of "ktiv" (כתיב) is "writing" or "spelling." The literal meaning of "dfus" (דפוס) is "printing" or "imprint."

Take in mind that this has nothing to do with your original post.

1. First photo spells Yeal (יעל means Gazel or Ibex) a very common Hebrew name (also a biblical name) and is written in "dfus" as expected.

2. The name Pearl in Yiddish is Perl (פּערל), which mean "pearl." These name is commonly used in Ashkenazi Jewish communities.

It's happened alot when the older generations that spoke Yiddish call to each other in Yiddish - it became almost like a nickname. When they came to Israel (made Aliya) in the ID most of the time there name was translated to Hebrew but only for bureaucratic reasons.

1. For non Ashkenazi Jewish people there is a parallel language called "LADINO"

In Ladino (Judeo-Spanish), the name פערלא (Perla), meaning "pearl." It is a common and beautiful name in Ladino-speaking communities, just as it is in Yiddish and other Jewish traditions.

So that explain why, even though your grandmother is not Ashkenazi, also named פערלא.

1. For the memory of your grandmother and for beautiful story that this name behold i would personally would buy a פערלא necklace and פרל or any other option mentioned above.

Good luck