Whilst it is better and more praiseworthy to give in charity in secret whilst the left hand does not know what the right hand has given. However we shouldn't have to go to such extremes as you are stating. As long as we ensure that we check our intentions beforehand (like we should do before every good action), then we can give publicly too whenever there is an opportunity to do so, as we do not want to miss any opportunity of giving in charity, as it will be a source of huge regret in the Hereafter.
When you're donating online then there's nothing to worry about when it comes to one's intentions. This is because admin knowing your details is irrelevant to your intentions as they do not know who you are. You are just another "number" in the thousands who've donated and whose transaction they are processing.
So there's absolutely nothing to be worried about in that regard. At times we have to try and distinguish between genuine concerns, worries and doubts and the insinuating whispers of shaythan (Waswasa) which is also linked to OCD. If this is something we think we may suffer from to some degree as many of us do, then please see the following thread:
How to Overcome Waswasa/OCD in Worship