I got a PCR test result to enter Thailand but it doesn't state my passport number. 

Just name and date of birth, and address in home country. 

(I will try to get a new one)

Anybody knows,  whether this is sufficient?  Or is the passport number in the PCR test result necessary? 

Your name should be sufficient. 

 

However, I never took the chance and simply edited my Passport number onto my PCR tests in the past. I also edited in my passport number into my Vaccine Certificate (Adobe Acrobat).

 

The key point with your PCR test certificate is to ensure it states RT-PCR as the testing method... (someone was recently refused entry upon arrival because their test didn’t state RT-PCR test).