I have no idea why Unity choose to not make its WebGL exporter default to filling the window like pretty much all other WebGL apps on the net but in any case here is a template
Example: https://greggman.github.io/better-unity-webgl-template/
Downloand and add in this unity package
into your project. Then pick Edit->Project Settings->Player
, in the WebGL tab
under Resolution and Presentation pick "BetterTemplate".
Change Assets/WebGLTemplates/BetterTemplate/logo.png
to whatever you want.
See Unity docs on how to customize WebGL Templates.