Rudra -Angry Lord Shiva-this one is pretty obvious, Rudra is one of Shiva's name, it means destroyer of evil. Rudra's most defining quality is his anger like Shiva's Rudra avatar. Like Lord Shiva's Rudra roop he also sets out to destroy evil in the form of terrorists mainly.
Parvati-Shiva's wife/one who lives in mountains -other half of Rudra, incarnation of Shakti. Parvati Maa was determined and it showed in her difficult penance to prove herself worthy of Shiv ji. Likewise Paro is also determined, tough to break, she is willing to go great lengths to win Rudra's love.
Dilsheer-lion heart- Dilsheer has had a hard life, his physical disabilities, insecurities, his wife abandoning him, living alone and bringing up Rudra, it's all been hard but he's brave in his own way much like a lion.
Mala -string/garland- a string is used to bind things together, a garland has its importance in tying to people in bond of marriage in Hinduism and Mala ties all the characters together in RR. She is the common link between the Ranavats and Tejawat, she in some way ties Rudra and Paro together, she is his mother and almost an adoptive mother to Paro.
Danveer -charitable- Danveer is very giving and in return demand very little. He gives Mala information about Rudra but never demands to know reasons behind her abandoning her family.
Mohini -enchantress- lol I don't know about how much of an enchantress she is but Mohini is but she knows how to manipulate and trick people and get her way. Lord Vishnu also took the form of Mohini during Samudra Manthan and tricked the demons.
Samrat-emperor- no idea why a guy like him who has no backbone would be given such a name lol so cant offer any kind of explaination.
Maithalli-goddess Lakshmi/Sita- Sita's life was a struggle especially after her marriage to Rama, Maithalli is always taunted for a situation that is not in her control like Sita was.
Sumer-friendly- I don't know how accurate this is, lots of sites where misunderstanding Sumer for Summer (a girl's name!) but one said Sumer means friendly, which he is to an extent I suppose.
Sunehri -golden- Sunehri's character is shown to be very warm, happy and friendly and the colour gold would round up those feelings and characteristics. Sunehri's character gives a warm golden vibe.
Amandeep(Aman)-light of peace- Aman seems a peaceful guy lol compared to Rudra, he works for BSD who want to maintain peace in the country and border
Laila-night beauty, nocturnal-LOL Rudra can answer this better than us but yeah again it fits her character, she's beautiful