The scene you need to look at is Act I scene 3, when Celia and Rosalind plan to go to the Forest of Arden together because Celia's father has banished Rosalind from court, just as he has already banished Rosalind's father, Duke Senior. Having already spoken of the necessity of disguising herself as a man to prevent their youth and beauty being even more of a danger than having money would be, Rosalind, according to pastoral conventions, says that she will call herself Ganymede when disguised. Ganymede was a beautiful young shepherd boy who was snatched away by Jove and taken to Olympus to be the cup-bearer of the Gods. Because of Jove's desire for Ganymede, the name also has strong homoerotic associtions.
The name that Celia chooses for herself is more obvious to us today, and something that she feels befits her new station now that she is leaving her home and going into the wilderness:
Something that hath a reference to my state:
No longer Celia, but Aliena.
Thus Celia chooses a name for her disguised identity reflecting that she is an "alien" away from her home and in the middle of the forest.
in the act 1 scene 3 Rosalind is asked by his uncle duke Frederick to banish from the court so Celia as a friend offers the plan to flee in disguise as "beauty provoketh more than gold". so Rosalind disguised as a shepherd with the name GANYMEDE which was the name of Jupiter's page who was also effeminate boy such as Rosalind. Celia was in a state of confusion so she kept her name as ALIENA when she disguised herself as a shepherdess
Rosalind gave herself the name GANYMADE when disguised as a male and Celia was named ALIENA
Rosalind assumes the name of "Jove's own page, Ganymede." This is for two reaons. Jove was the king of classical Gods in Greek Mythology who fell in love with a handsome young boy called Ganymede and then carried him to Mount Olympus to make him his cup-bearer. Ganymede was handsome but effeminate which describes Rosalind in disguise as she would be a lady dressed as a man. The second reason is under lying in the words, "Jove's own page." The word Jove means fortune and page is a servant. Rosalind, in her current situation is a servant dependent on fortune.
Celia assumes the name Aliena which literally means stranger. She does so since this name righteously describes her situation, i.e., once she enters the Forest of Arden, she would be a starnger to it. The second reason is that she was now enstranged from her father, Duke Frederick.
Rosalind, the daughter of the banishes Duke Senior, is forcefully banished by her uncle Duke Frederick, who had unlawfully usurped her father's kingdom. She dons the "doublet and hose", and disguises herself as a young boy, before leaving for the fprest of Arden, which was to be her site for refuge. She names herself Ganymede.
Ganymede, according to Greek legend, was a Trojan man of wondrous beauty. Because of this, he was abducted by Zeus (who has disguised himself as an eagle) and taken to Mount Ida (the abode of Gods), to be the cupbearer of the Gods. Rosalind finds herself in a similar situation. She is forced to leave her lawful residence, but hopes to be happier at her new residence. Just like Ganymede was granted the boon of eternal youth and life, Rosaling also hoped to lead a more contented, peaceful and meaningful life in her new refuge. Because of the similarities in the predicament of Ganymede and herself, she christens herself as Ganymede.
Celia, Rosalind's cousin and Duke Frederick's daughter, decides to accompany her beloved sister. She names herself "Aliena"-- because she is now an alien. It is only out of sheer love for her sister that she decide to accompany her to exile. But she does not willingly belong to their pastoral refuge, the forest of Arden, where she must wander about like an alien- her true identity knowm only to Rosalind. Moreover, she is also like an alien to her father's court, now that she decides to elope. She thus names herself as "Aliena".
Hnece, the two sisters name themselves according their own predicaments.