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

No.

While the spelling, meaning, and grammatical identity of "tenho" (the first-person singular of the verb ter) are identical in both dialects, there are differences in typical usage and pronunciation:

• Typical Usage: In Brazil, when expressing obligation (the "have to" construction), it is much more common to use the preposition que (e.g., tenho que fazer). In Portugal, the standard and more natural usage is with the preposition de (e.g., tenho de fazer).
• Pronunciation: In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels undergo significant reduction; the "e" in "tenho" is often shortened or almost silent, making the word sound much more closed and clipped.

Brazilian Portuguese Usage

1. Eu tenho um carro novo. (I have a new car.)
2. Tenho que fazer o dever de casa. (I have to do my homework.)
3. Tenho muita vontade de viajar. (I really want to travel.)
4. Não tenho nada para comer. (I have nothing to eat.)
5. Tenho que te ligar mais tarde. (I have to call you later.)

Continental Portuguese Usage

1. Eu tenho um carro novo. (I have a new car.)
2. Tenho de fazer os trabalhos de casa. (I have to do my homework.)
3. Tenho muita vontade de viajar. (I really want to travel.)
4. Não tenho nada para comer. (I have nothing to eat.)
5. Tenho de te ligar mais tarde. (I have to call you later.)