I have weird problen while sending link to my site on discord app in attachment is photo with what i see while sending link do my website.
Under site name is "admin" link which redirect to specified admin account profile on forum, how can I remove that thing from link and make it show website logo or something?
This is the author of your forum page in WordPress system. If you edit the forum page using [Edit Page] link in the black top admin bar, you'll be able to manage the author name. However, I'd recommend managing the SEO plugin and disable showing the author data in SEO Meta tags.
I assume you have a SEO plugin which provides author details to page crawlers/indexers/sharing bots, so you should disable this option. This could be found either in the SEO plugin settings or in the Forum Page editing screen.