The CDU is a large party, not a particular large "organization" in terms of full-time CDU employees. The bureaucracy of the CDU is in no way responsible for nominating/selecting the EU President of the Commission.
Ursula on der Leyen was 2019 supported by Angela Merkel (Chancellor of Germany) as the future president of the EU commission. That's no secret. Macron also supported her. The European Council then nominated Ursula on der Leyen and she was accepted by the European Parliament. The Parliament is directly elected the citizens of the European Union.
The election of her was kind of unfortunate, since it was signalled by parties that the election to the parliament will also find the proposed EU commission president. But that was not the case. Since a candidate was not found (various parties and governments were not happy with the proposed candidates), the European Council finally proposed Ursula von der Leyen, which then also got a majority in the parliament.
It's not clear who specifically did the ceremonial nomination, but it was probably the CDU bureaucracy that made the decision.