No, custom logos and contest branding are not currently supported for private (self-managed) contests.
Current Status
This feature was available in previous seasons
It is not available this year for formats
Alternative Option
If you would like to:
Add a custom logo
Brand your contest
You will need to create a Splash-managed (real-money) contest, where branding is supported.
Summary
Private (self-managed) contest: No branding or logo support
Splash-managed contests: Branding available
We understand this change may be unexpected and appreciate your feedback as we continue improving the platform.