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

Yes

The word "pereira" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open and the rhythm is more syllable-timed, meaning each syllable is clearly articulated. In Continental Portuguese, the rhythm is stress-timed, and unstressed vowels undergo significant "vowel reduction," meaning they are shortened or almost swallowed.

Brazilian Portuguese

1. Tem uma pereira no jardim. (There is a pear tree in the garden.)
2. A pereula está dando muita pera. (The pear tree is producing a lot of pears.)
3. Eu plantei uma pereira ontem. (I planted a pear tree yesterday.)
4. A pereira está morrendo por falta de água. (The pear tree is dying from lack of water.)
5. Você viu a pereira? (Did you see the pear tree?)

European Portuguese

1. Há uma pereira no jardim. (There is a pear tree in the garden.)
2. A pereira está a dar muita pera. (The pear tree is producing a lot of pears.)
3. Plantei uma pereira ontem. (I planted a pear tree yesterday.)
4. A pereira está a morrer por falta de água. (The pear tree is dying from lack of water.)
5. Viste a pereira? (Did you see the pear tree?)