I have the problem that the logo of the webpage is shown very well when its a normal size of page. When I resize the screen so that the small logo and the off canvas menubutton is shown the, the background of the logo is not only the normal background but overloaded by the background of the navbar (.uk-navbar color). Did i do some wrong configuration, or how can enable that this background is not shown here.
Live page to see: www.tbc-schwimmen.de/

No there is nothing wrong.
The logo is always placed into the menu bar...
Look to the org theme, here it is the same.

Thanks, so I understand therefore seems no possibility to omit the nav background color in the small resolution

The navbar background is the background you have setup, in your case its blue.
Maybe you should use another logo for small devices.

I got now the effect i wanted by custom.css
ul.uk-navbar-nav.uk-hidden-small {
background: #2243aa;!important;
z-index:99;
}
.uk-navbar {
background: rgba(34,67,170,0);
}
With this css on small resolution the logo is shown without background color because of transparency on nav menu. So I can see the background image. On mormal resolution the nav has the wanted color