"And she said, Behold my handmaid Bilhah" (Genesis 30:3). [Her name Bilhah is] like the word behalah (alarm), for she would become alarmed at the time of her giving birth and did not know how to nurse. And our Sages, of blessed memory, said that the four of them were sisters, for Jacob was not permitted to marry a maidservant; rather they were from another wife, and Laban loved Leah and Rachel more than them, and so he called them maidservants.
Why Bilhah Was Named for Panic and Called a Maidservant
Midrash Aggadah, Genesis 30:3
ותאמר הנה אמתי בלהה. כעין בהלה שהיתה מתבהלת בשעת לידתה ולא ידעה להניק. ואמרו חכמינו ז"ל כי ארבעתם היו אחיות, שלא הותר ליעקב לישא שפחה, אלא היו מאשה אחרת, והיה לבן אוהב ללאה ולרחל יותר מהן וקראן שפחות: