"I would like to open a account at Commerzbank"
Wie kann man das sagen?
Ist es: "Ich möchte ein Konto bei Commerzbank eröffnen" Oder: "Ich möchte ein Konto bei Commerzbank einrichten"
That entirely depends on the manner in which the sentence would be used. If they need to write it in a letter or say it to someone, specifying the bank isn't just preferable but necessary.
To me, it sounded more like a request, but you're right pointing out other possible scenarios. In yours it can be a useful piece of information, I don't agree on the necessity of said precision :)
I'm not German, and I'm not sure, but I would pick "eröffnen" because einrichten is more like furnish, furnish a room with furniture.
How about simply öffnen?