About Jewish Birthdays
Ironically, the one birthday mentioned in the Torah is that of Pharaoh (Genesis 40:20-22). To celebrate, Pharaoh hosted a feast, and made a personal accounting of his life.
Through this example, we can deduce the proper way to celebrate a birthday: introspect and take stock of life. Think about all the positive things that happened in the past year, as well as the mistakes, make a commitment to improve. Express gratitude to God for being alive and healthy, and gratitude to your parents for giving you life. And of course, enjoy some chocolate cake and ice cream.
The traditional greeting to give someone on their birthday is: May you live to 120. This is because Moses, the greatest Jewish leader, lived till the day of his 120th birthday.
About Jewish Names:
A Jewish name is profoundly spiritual. In Hebrew, a name is not merely a convenient conglomeration of letters. Rather the name reveals its essential characteristic. The Midrash tells us that the first man, Adam, looked into the essence of every creature and named it accordingly. The same idea applies to names of people. For example, Leah named her fourth son Judah (in Hebrew, Yehudah). This comes from the same root as the word "thanks." The letters can also be rearranged to spell out the holy Name of God. The significance is that Leah wanted to particularly express her "thanks to God." (Genesis 29:35)
Ashkenazi Jews have the custom of naming a child after a relative who has passed away. This keeps the name and memory alive, and in a metaphysical way forms a bond between the soul of the baby and the deceased relative. Sefardi Jews also name children after relatives who are still alive.
Some customarily choose a name based on the Jewish holiday coinciding with the birth. Similarly, names are sometimes chosen from the Torah portion corresponding to the week of the birth. Many names and events are mentioned in each Torah portion, offering a spiritual connection between the baby and that particular biblical figure.
Ultimately, it's what you make of your name that counts. For at the beginning we are given a name, and at the end of life a "good name" is all we take with us.
See more at: Naming a Baby