Hi Matthias,
Sorry for the delay in response.
You do not need to declare, for which project you want to use the Adobe Stock image. You can use the same license twice, however, please make sure that if you are using the same asset for different clients, the asset should be licensed separately so that it is legitimate.
For more information on the usage of Adobe Stock images for client use, please seehttps://wwwimages2.adobe.com/content/dam/acom/en/legal/servicetou/Adobe_Stock_Additional_T erms_en_US_20180605_2200.pdf (Section 3.4 a)
If the asset is to be used by your client, I would suggest you to have the license transferred to your client in order to prevent confusion wherein the client needs to sign a written statement indicating that they will follow the stipulation in the Stock licensing Term.
Note: We do not offer exclusive licenses.
You may also refer to Common Questions, Adobe Stock for more information.
Hope this helps!
Feel free to update this thread in case of any additional questions.
Regards,
Twarita