There's a number of ways to deal with this.
Normally in template projects the logo will be precomposed so that all animation happens in different comps. As a result, you can simply drag your new logo into the timeline, then turn off or delete the original logo layer. Scale your new logo layer so that it's around the same size as the original.
Alternately, select the original logo layer in the timline. Then import your new logo into the project window, hold down the Alt/Option key and drag the new logo from the project window onto the selected layer in the timeline to replace it.
To completely replace the logo, right click on it in the timeline and choose "Reveal in Project". This will highlight the logo source file in the project pane. Right click on this and choose "Replace footage item".