Johnson & Johnson vaccination

This website gives you the answers.
https://www.germany.info/us-en/covid-19/2321562

The Janssen vaccine listed as approved for Germany is the same as Johnson and Johnson.

Here is quote from this website. I encourage you to read the website for yourself.
Individuals aged twelve years or older are under a general obligation to provide COVID proof when entering Germany. Upon entry into the Federal Republic of Germany, individuals aged six years or older need to be in possession of proof of testing, proof of recovery or proof of vaccination. As a general rule, COVID tests (antigen tests or PCR tests) must not be older than 48hrs at the time of (planned) entry into Germany. When using a carrier (e.g. an airline) PCR tests must not be older than 48hrs at the time of (planned) departure; antigen tests must not be older than 48hrs at the time of (planned) entry into Germany even when using a carrier.

The obligation to provide COVID proof also applies to airline passengers only transiting at an airport in Germany. This applies to both the non-Schengen transit from and to third countries outside the Schengen area and to the transit from and to Schengen countries.

Proof of testing, proof of recovery or proof of vaccination must be presented to carriers for review prior to the journey. Only in the event of cross-border rail transportation or cross-border short sea shipping proof may also be presented in the course of the journey. Furthermore, upon entry into Germany, proof has to be presented to German border control authorities upon their request.

I have taken the J&J vaccine and have a J&J booster, do I still need to a negative test, to transfer though the Berlin airport, on the way to Rome?

Yes. Germany does not consider you to be fully vaccinated at this time with just 2 shots (even with J&J). This was not the case before but the rules changed. So unless you can get a 3rd shot not later than 14 days before you leave, you should be prepared to have a negative (PCR) Covid test with you.