Typically, Shakespeare isn't into assigning heavily symbolic names but he does put some thought into what he calls his characters. When Rosalind dresses up as a boy and calls herself "Ganymede," we can't help but think of the Ganymede from classical mythology, the pretty boy who was kidnapped by Jove and turned into a love slave. In Elizabethan England, the name "Ganymede" was a term applied to young men who had affairs with older guys so, Shakespeare is definitely raising the possibility of same-sex desire here. This becomes obvious when Orlando pretends to woo "Ganymede" and when Audrey falls in love with "him."
The name Celia chooses when she disguises herself is significant, too. "Aliena" (as in alien) means "estranged one." Estranged and alienated is exactly what Celia is when she runs away from her father's court to be with her cousin.
The de Boys family's old servant Adam has a biblical name that's pretty meaningful. In Genesis, Adam is the first man, and we associate the name with old age and the origins of humanity. (This is fitting, because Shakespeare's Adam is insanely old, and the Forest of Arden recalls the Garden of Eden.) Also, the biblical Adam is the father of Cain, who murdered his little brother, Abel. Hmm. This sort of reminds us of Adam's involvement in the whole Orlando/Oliver feud.
The pastoral setting should free us from having to worry about the constraints of the court. Still, many of the court's characters are arrogant about their social status and their home town. Note how Touchstone greets Corin, a stranger to him, when he is in dire need of some hospitality:
Holla, you clown!
Peace, fool; he's not thy kinsman.
Your betters, sir.
Else are they very wretched.
Touchstone is in turn put down. When Jaques introduces him to Duke Senior, Jaques laughs heartily at the idea that Touchstone had been "at court." Jaques knows Touchstone's court position as a lowly fool, and as a lord can stand on it mockingly. The fool is not to be pitied. He did the same thing to poor Corin, who was guilty only of being unschooled in the way of the court. Being so ignorant of court ways, all Corin can tell is that anyone from court is higher than he and, rather than reply as a free man of the forest, he subjects himself to the fool. Status only matters if those around you think it matters, too.
Interestingly, it is those with the most claim to titles that are most humble about it in the forest. Rosalind considers herself an exile more than a princess, and becomes happily involved in love-matches over things like court-matches (which aim for prestige instead of warm and fuzzy feelings). Orlando, while he originally wanted education and training befitting a gentleman, conspires with Adam to seek a lowly life of contentment in the forest. Even when Jaques would have him commiserate about the world, Orlando says he thinks ill of none but himself, whom he knows best. This is pretty significant, as both his experience and his status as a nobleman would easily let him condescend to others. Yet the exiled Duke might be the best example of grace under lost titles. When we meet the Duke, he says he's glad to leave the pomp of the court, as it is in the forest that he is reminded that he's only one of many men on earth:
And churlish chiding of the winter's wind,
Which when it bites and blows upon my body,
Even till I shrink with cold, I smile and say
'This is no flattery; these are counsellors
That feelingly persuade me what I am.' (2.1.3)
It seems that Shakespeare is using status as a mark, both of nobility and of shame. Those who actually deserve their noble titles would let them drop away upon entry to Arden; their graciousness and nobility is in their nature. The others who would cling to their tiles, or judge others by them, are less to be respected, as they've learned less (and are worth less) in both settings.