The general principle regarding names in Islam is that they are permissible unless they contain one of the following:

A meaning that is exclusive to Allah.
A meaning involving worship of other than Allah.
An explicitly idolatrous or polytheistic meaning.
A meaning that is obscene, degrading, or otherwise objectionable.
As for names whose origins are ancient, disputed, or linguistically uncertain, the scholars generally look at the meaning by which the name is known and understood among people, not every speculative etymological theory that may be proposed centuries later.

Regarding Julia:

The name Julia is widely understood today as a personal name without any intention of worship, divinity, or pagan devotion. The commonly cited meaning is “youthful” or “young.” While some historians and linguists have discussed possible ancient connections between the Roman family name Julius and other roots, including theories involving Jupiter, these are matters of historical etymology and are neither the commonly understood meaning of the name nor an intended religious reference when parents name a child Julia.

Therefore, the stronger view is that Julia is a permissible name, because people using the name neither intend nor understand it to mean devotion to Jupiter or any Roman deity. The mere existence of a disputed historical theory does not make a name prohibited.

Similarly, regarding Yara:

Names can have different meanings in different languages. The relevant question is: what meaning is intended and understood by the people using the name?

If a family chooses the name Yara because of a permissible meaning known in their culture, such as a beautiful or positive meaning, and they are not naming the child after a deity nor intending a pagan religious reference, then the name is generally permissible.

The fact that a similar sound or spelling may have a mythological meaning in some other language does not automatically render the name forbidden. Otherwise, many common names used throughout the world would become problematic simply because they happen to resemble words in unrelated languages.

At the same time, the Office of the Imam of IAR generally advises Muslims to choose names that are:

clearly good in meaning,
free from ambiguity,
and connected to righteous people, prophets, companions, or noble Islamic qualities whenever possible.
This is the safest and most virtuous approach.

However, based on the information you provided:

Julia is permissible, and the speculative Jupiter theory does not make the name prohibited.
Yara is permissible when used with a permissible intended meaning and not as a reference to a deity or goddess.
Neither name would be considered impermissible merely because of an uncertain or unrelated meaning found in another language or culture.