watermark of my site on photos purchased with standard license

This looks complicated. You cannot claim being the creator of the asset. You can, however, watermark it appropriately. Anyhow, you won't put a full resolution picture on your site. That too is a good protection.

Look here for more information on licensing: https://community.adobe.com/t5/stock/links-for-licensing-terms/td-p/11366788
(Disclaimer: As always with licensing, this is my interpretation of the rules. I think they are correct and advice is based on reading and interpreting the licence terms and on fair use for both the buyer and the artist/stock company, but I cannot rule out that my interpretation is wrong. I'm not an Adobe employee).

This is a Stock user question, not a Stock Contributor question.  I am moving this post to Adobe Stock.

As far as I know, you are allowed to alter the photos. But to be sure, please check your license agreement.

As a contributor, I dont want to see your name on my photos. Even though you bought it, it belongs to me. Put my name on the photo! Problem solved.