Navigate to the Assets tab in the left hand navigation bar.
Click on the competition for which you want to change the logo. In the below image American Football Festival is the competition.
Hover over the competition logo and select Replace.
Navigate to where the new logo is located.
When happy, select Open or double click on the desired logo.
Once selected you will enter the Edit Image section. Position and scale the logo as required.
Once happy, hit Save.
Hit Save at the next screen and you have successfully changed the competition logo.