The Grammy-winning band behind hit songs including “Need You Now” and “Just a Kiss” changed their name last month, also to Lady A.
While the decision was made due to their original name’s connotations with the slavery era, the band were soon criticised for choosing a name already in use by a black artist.
They claimed they had attempted to resolve the dispute with Lady A, real name Anita White, in an amicable manner. However, they alleged that her team demanded a $10m (£7.9m) payment in return for their use of the name.
According to papers filed in Tennessee, the country band are not demanding money from White and insist she will be able to continue performing under the name.
The purpose of the case is mainly to assert their rights to the Lady A trademark, which they say they have held since 2011.
White told Variety that she expected the band to take legal action because they seemed “unwilling to compromise” from the beginning. She said she had planned to donate half of the $10m to charities of her choice.
“I think they always knew what they were gonna do,” she said. “I was quiet for two weeks because I was trying to believe that it was going to be OK and that they would realise that it would be easier to just change their name, or pay me for my name.
“Five million dollars is nothing, and I'm actually worth more than that, regardless of what they think. But here we go again with another white person trying to take something from a black person, even though they say they're trying to help.
“If you want to be an advocate or an ally, you help those who you're oppressing. And that might require you to give up something, because I am not going to be erased.”
Lady A the band have yet to respond to White’s latest comments.