Disclaimer: The names below have multiple meanings, in Sanskrit, Hindi and other Indian languages. I have selected the most common/well-known meaning of the name; or in some cases a meaning that proves my point better than the common/well-known one ;-) (claiming writer's privilege here!)
Arti - worship of God; in Hinduism, the key/main part of the worship is called Arti
So obviously, Arti is the key or heart of the show. As her name implies, Arti worships God - both the omniscient form (almighty) as well as her "god on earth" - aka family. Worship defines her to be humble - to the point you want to shake her at times. But aren't all God's best known devotees also his most humble ones? Humility is the key (that word again) of devotion - and Arti, the character, personifies devotion. Be it devotion to God, to her family (parents, in-laws), to her children or to her Yashji. And this devotion drives all her actions - her blind faith on her loved ones, her going out of the way to help her family, her unending stream of love and caring even towards those who have, and continue to hurt her.
Gayatri - personification of the Gayatri Mantra, one of the most revered mantras in Hinduism; used to pray for wisdom, strength and spirituality
One of the most religious characters in the show - perhaps the most spiritual as well? Her belief in the almighty has helped her weather all storms. A woman whose purpose in life, whose existence is through her husband and her children - today she stands at the cusp of something with the potential to tear her world apart. Will the woman who has the ability to inspire strength in her family, find her own inner strength, her own Gayatri, to fight the biggest battle of her life?
Vidhi - principle, law, tradition.
Vidhi - the eldest daughter-in-law. In many ways, the most difficult position in the family. The first one who enters the family-fold in each new generation, the one who helps define what the traditions will be. The one who is responsible for maintaining that tradition, the one who has to be the principled one, the one who has to de-facto lay down the law for those coming after her. And Vidhi upholds each one of these expectations - sometimes to the extent of going to extremes.
Paridhi - measure, restriction, extent / limit.
This was one name I did not know and the meaning astounded me. This one convinced me that the Mittals or CVs, or someone in the PV-makers camp is indeed naming their characters after much thought and deliberation. Paridhi is the one bahu that defied restrictions, tried to break through the barriers and establish new limits. And despite being the youngest, she has the true measure of each character in the family - she understands what drives each person. Its her goodness that she does not exploit her knowledge - again, staying within her limits.
Maya - illusion
In how many ways do I explain thee??? Maya bua - obviously holding up an illusion of goodness. Her heart filled with jealousy towards her family, yet portraying that she has their best interests in mind. How strong is your family bond? Only as strong as the weakest link in the chain. And Maya is the weakest link in the Scindia parivar. If another "villain" were to tap into her - what a powerful combination would they make...Maya maintaining her illusion of caring and well-being while viciously providing input to the "villain". Stuff for a great thriller/revenge-tale and another show altogether :-).
Shobha - pride, beauty
One of the most complex characters in the show - Shobha encapsulates pride and beauty within herself. Pride at being the perfect mother, and her true beauty lies in her ability to love others like her own flesh and blood. One (pride) precluded her from seeing the real pain and issues her own son faced; the other (beauty) enabled her to empower an orphan, devastated woman like Arti and an equally rudderless and drowning in grief Yash, to find each other, accept each other and build their lives anew. And someone who helps others rebuild their lives are a true "shobha" are they not? Except in her case, her pride led to her, and by extension her immediate family's downfall...
Radha - success
Ah - currently the most intriguing character in the show - and the one who got me thinking about the names and their implications on the character. The way we know "Radha" - she defines love in its purest form, she is the consort of Kanha - the only couple in Hindu religion accepted and worshiped as a couple, even when they, in legal and social terms, are not a "couple" (aka married to each other). Foreshadows of the story to come...? Time will tell.
And success? Who knew the name meant success? Does that mean she will succeed in her goals? But - and this is the crux, isn't it - what are her goals?
Remember though - Radha is known as the epitome of love - and she can never be evil...
Ishita - greatness, superior
Appropriate again??? Ishita obviously comes from a much more wealthy and influential family than the one she inadvertently married into. And does she have a superiority complex? One wouldn't think so given her life, her handicap - but these things are way more complex than they appear on the surface. Ishita holds / will hold, even more than Radha, the power to harm the Scindias - and her target will be ArYa. Will she team up with Maya? That would be interesting indeed...
Arpita - dedication (to the divine)
Ironic - that both of Yash's wives have names with very similar meanings? I think not. A deliberate choice showing how alike - in character, in giving primary importance to family, in their capacity to love - the two women who redefined Yash's life, are. Yash learned to love from Arpita (dedication) and learned how to sustain that love from Arti (devotion). If this were real life - it would be termed divine providence. Since its a show - let's call it the Mittals' vision.
In short, analysis result: the names mold the characters.
Feel free to add to this, disagree, discuss, etc. My little bit to help increase the activity on the forum.