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

Yes

The word "pendurar" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The differences between the two varieties are purely phonetic (Continental Portuguese features "vowel reduction," where unstressed vowels like the 'e' are much more closed or nearly silent compared to the more open vowels in Brazil) and contextual (the way the verb is used within a sentence, such as the choice of subject pronouns or related vocabulary).

Brazilian Portuguese (Natural Usage)

1. Eu vou pendurar o quadro na sala. (I am going to hang the painting in the living room.)
2. Não esquece de pendurar a toalha depois do banho. (Don't forget to hang the towel after the shower.)
3. Ele pendurou a camisa no cabide. (He hung the shirt on the hanger.)
4. Ela gosta de pendurar fotos na parede do quarto. (She likes to hang photos on the bedroom wall.)
5. Você pode pendurar a mochila ali? (Can you hang the backpack there?)

Continental Portuguese (Natural Usage)

1. Vou pendurar o quadro na sala. (I am going to hang the painting in the living room.)
2. Não te esqueças de pendurar a toalha depois do banho. (Don't forget to hang the towel after the shower.)
3. Ele pendurou a camisa no cabide. (He hung the shirt on the hanger.)
4. Ela gosta de pendurar fotografias na parede do quarto. (She likes to hang photographs on the bedroom wall.)
5. Podes pendurar a mochila ali? (Can you hang the backpack there?)