Some relatives insists that the name Nayla is not good for a girl.They narrate a story of beautiful lady with the same name who was worshiped before the advent of Islam.Some say, a lady of same name was a street girl.For me these seems baseless. Would you kindly highlight the specific nature of the name : Nayla.

Nayla was the name of the wife of Uthman ibn Affan, she was a Christian woman who was converted to Islam under the guidance of Aisha, wife of Prophet Muhammad ﷺ. If there was anything wrong with her name she would have been asked to change her name. There are also female Sahabiyyaat (righteous women who lived at the time of the Prophet) with the name Nayla, such as Nayla bint ar-Rabee', Nayla bint Salaama and Nayla bint Saad bin Malik, all of whom went to the Prophet and gave the Shahadah (the oath of becoming Muslim). If the Prophet ﷺ did not like a person's name due to its having a bad meaning, he would change the name. But he didn't change the names of these Sahabiyaat, which shows that there is nothing wrong with the name.

Nayla was also the name of one of the pagan goddesses that were worshiped by the people of Makkah. This doesn't automatically make it a bad name. We also know that Jesus/Isa is worshiped as a god by some Christians, this doesn't make Jesus/Isa a bad name. And the false god al-Laat is actually the name Allah with a "t" added to the end to make it female, this doesn't make Allah a bad word.