When I was born, my parents gave me three different names. Two are on my birth certificate, and one is the name they gave me in shul (synagogue).
The first name on my birth certificate is simply a name my parents liked, and that is what they, and everyone else, called me for
The second name on my birth certificate is my grandmother's, z"l*, English/secular name. No one ever called me by that name (except my mother, when she was very angry at me; then she would call me by my first, middle and last name!). Still, I was very conscious that I was named after my grandmother. And, occasionally, I did have to sign something using either my middle name or middle initial.
Rivka was my grandmother's Hebrew/Jewish name. No one ever called me, or her (as far as I know), by that name either. Everyone used our English names.
In college, I questioned the meaning of being named after someone if no one uses that name. In another generation, the name disappears and the continuity is broken.
I decided to honor my grandmother by using her name, Rivka.
I did not ask people who knew me before to change the way they called me. I was not rejecting my "old" name, but, rather, embracing both my grandmother and my Jewish identity.
Some friends chose to call me by both names. I did not mind, but I did find it somewhat amusing, and long.
A few months after I started using the name Rivka, an Israeli friend showed me the way the name is pronounced in the Torah. It was the first grammar lesson that ever interested me. Though most people today pronounce Jewish names mil'el (with the accent on the first syllable), in the Tanach, all names are pronounced mil'rah (with the accent on the final syllable)**.
The proper pronunciation not only sounded prettier to me, but it also felt stronger, less galus-dik. Ironically, the ancient pronunciation felt more modern to me. Thus, RIV-ka, became Riv-KA. (At the time, I was very influenced by the Israeli short story, The Name, by Aharon Megged. For a short summary and an interesting analysis of the story, see here.)
Though I never asked people to call me by my "new" name, I did (and still do) insist that people pronouce my name correctly.
I am glad that there are still people, primarily family and old friends, who call me by the name of my childhood. I love that name, and it is a part of who I am. Moshe, who knows me since we are 15, still calls me by that name. I like to say that name is "my family name," used by both my old family, and my new one.
RivkA is the name by which the universe knows me. RivkA is my Jewish name, the name which connects me to God, the name used by all those who pray for me around the world.
My name is RivkA, daughter of Teirtzel and Yeshaya HaLevi.
Please daven (or send happy, healing thoughts) for RivkA bat Teirtzel.
With love and optimism,
*z"l = zichronah livracha, may her memory be a blessing.
** For a more in depth discussion about Biblical grammar and Biblical names, see The Dikdukian