Hi Maria Valek , Welcome to Microsoft Q&A platform and thanks for posting your question here. It sounds like you are experiencing issues with the parallelism of your pipeline. It's possible that multiple instances of the copy activity are trying to write to the same blob storage location simultaneously, causing conflicts and incorrect naming or missing files.
Instead of timestamp , you can try distinguishing the sink file names with unique identifier values which can be generated with the help of guid() function.
Kindly try if this works fine for you. Else, try making the timestamp value more and more precise so that it doesn't generate same sink filename for two instances of iteration. Otherwise, running sequentially would be the only way out. Hope it helps. Kindly let us know how it goes. Thankyou