Re: my baby girl will be nameless 
Yanzala, take as an example the name Abid or Abida. This name means ibadat/worship/worshiper. But it doesn’t specifically mean Allah ki ibadat or worshiper of Allah. But the parents who give this name to their child would have the intention of it being Allah’s worship. The name Dua means prayer, but it doesn’t specifically mean Allah se dua karna. Afterall Hindus n Jews n Christians n Buddhists make dua too. But the intention as to who the dua is made too depends upon the parents’ religion. If they are Muslim, then naturally they see dua as prayer made to Allah alone. Tum kuch zyada nahi soch rahay/rahi?
Make sure that Anabia does indeed mean ruju because some of these websites …you can tell that there’s no certainty with the meanings…like a name such as a Farzana can mean mean beautiful and wise and neither of these two adjectives have anything in common. So, make certain of the meaning and clear your doubts about the permissibility of the name with an imam maybe.