Yes “Rent-a-Jew” also sounds like the person just needs to be Jewish.
In that case any Jew would do.
However surely they choose individuals capable of making personable and pleasant impressions, with strong and positive Jewish identities, who are also halachically Jewish.
Once I called “The Jewish Number” hoping to speak to a random Jew from around the world (that’s how it’s advertised). Turned out to be a not so random rabbi.
Rent-a-Jew reminds me of Simon Wiesenthal’s, The Sunflower, where a dying Nazi man asked a nurse to bring him “a Jew” any Jew, so he could ask “the Jew” for forgiveness for killing Jews.
The company’s name feeds into the dehumanization of being Jewish. Then again, it’s a business.
Maybe we would have to be there to get it.