Is the word júlia the same in Brazilian and European Portuguese?

Yes

The word "júlia" is a proper noun (a female given name), and its meaning, spelling, and grammatical function are identical in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazil, vowels are generally pronounced more openly, and the rhythm of speech is more melodic and syllable-timed. In Portugal, unstressed vowels are often reduced or "closed," and the rhythm is more stress-timed, which can make the word sound more clipped.

Brazilian Portuguese Examples

1. A Júlia é minha melhor amiga. (Julia is my best friend.)
2. Eu vi a Júlia no shopping ontem. (I saw Julia at the mall yesterday.)
3. A Júlia está estudando muito para a prova. (Julia is studying a lot for the exam.)
4. Você já falou com a Júlia hoje? (Have you spoken to Julia today?)
5. A Júlia esqueceu o celular no carro. (Julia forgot her cell phone in the car.)

Continental Portuguese Examples

1. A Júlia é a minha melhor amiga. (Julia is my best friend.)
2. Vi a Júlia no centro comercial ontem. (I saw Julia at the shopping mall yesterday.)
3. A Júlia está a estudar muito para o exame. (Julia is studying a lot for the exam.)
4. Já falaste com a Júlia hoje? (Have you spoken to Julia today?)
5. A Júlia esqueceu o telemóvel no carro. (Julia forgot her mobile phone in the car.)