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

Yes

The differences between the word "Maria" in Brazilian and Continental Portuguese are exclusively phonetic. In Brazilian Portuguese, the unstressed vowels are more open and clearly articulated; the "a" in "Maria" is typically pronounced as a bright [a]. In Continental Portuguese, unstressed vowels undergo significant reduction. Consequently, the first "a" in "Maria" is often pronounced as a closed, neutral "uh" sound ([ɐ]), and the final "a" is also more closed and less resonant.

Brazilian Portuguese

1. A Maria é muito legal. (Maria is very nice.)
2. Não seja uma Maria vai com as outras. (Don't be a follower.)
3. A Maria está descansando agora. (Maria is resting now.)
4. Aquela menina é uma Maria sem braço. (That girl is acting innocent.)
5. A Maria é uma menina muito inteligente. (Maria is a very intelligent girl.)

Portuguese (Continental)

1. A Maria é muito porreira. (Maria is very cool.)
2. Não sejas Maria vai com a outras. (Don't be a follower.)
3. A Maria está a descansar agora. (Maria is resting now.)
4. Aquela rapariga é uma Maria sem braço. (That girl is acting innocent.)
5. A Maria é uma rapariga muito inteligente. (Maria is a very intelligent girl.)