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

Yes

The word "guilherme" is a proper noun (a name), and its spelling, meaning, and grammatical function are identical in both Brazilian and Continental Portuguese. The only difference is pronunciation:

• Brazilian Portuguese: The vowels are more open, and the final "e" is typically pronounced as a clear, soft "i" sound (e.g., ghee-LHER-mee).
• Continental Portuguese: The pronunciation is more "closed" and consonant-heavy. The final "e" is extremely reduced, often sounding nearly silent or like a very short, neutral vowel (e.g., ghee-LHER-m).

Brazilian Portuguese Examples:

1. O Guilherme é meu melhor amigo. (Guilherme is my best friend.)
2. Eu vi o Guilherme no shopping. (I saw Guilherme at the mall.)
3. O Guilherme trabalha na padaria. (Guilherme works at the bakery.)
4. Você conhece o Guilherme? (Do you know Guilherme?)
5. O Guilherme esqueceu o celular. (Guilherme forgot his cell phone.)

Continental Portuguese Examples:

1. O Guilherme é o meu melhor amigo. (Guilherme is my best friend.)
2. Eu vi o Guilherme no centro comercial. (I saw Guilherme at the shopping center.)
3. O Guilherme trabalha na padaria. (Guilherme works at the bakery.)
4. Conheces o Guilherme? (Do you know Guilherme?)
5. O Guilherme esqueceu o telemóvel. (Guilherme forgot his mobile phone.)