The main ILIAS icon is stored in the images Directory as "HeaderIcon.svg". You con replace this easyly by your own Icon in svg format.

As long as your Icon is close to a square, this may be all that is needed. Probably you want to change the file favicon.ico in ILIAS' root directory too.

Non-sqare icons may appear very small in your Installation. To change this behaviour, some adjustmants have to be made in the less files

1. less/Services/MainMenu/delos.less:

Search for ilTopNav an change the margin from 65 to a wider value (e.g. 145 px, probably not needed if you use the standard right-bounr menu)Search for ilMainHeader and accomodate the width of the img entry some lines below (e.g.135px)

These settings fix the icon display for standard screens

2. less/Services/MainMenu/delos_sm.less:

To adjust settings for narrow displays (like smartphones), this file has to be edited.

You can search for "button.navbar-toggle" and set the left to an appropriate value (e.g. 135 px again)
or clip your Icon using and adjust ilMainHeader - img - width accordingly

-webkit-clip-path: polygon(0px 0px, 40px 0px, 40px 40px, 0px 40px,0px 0px);
clip-path: url("./square.svg#clipsquare");

for the ilMainHader img setting. webkit browsers can use the polygon directly, at the time of this writing firefox has to read the values from a seperate file with content like:
(opening brackets have to be inserted at the beginning of each tag)

svg xmlns="http://www.w3.org/2000/svg" class="clip-svg">
   defs>
       clipPath id="clipsquare"> 
               polygon points="00 0, 60 0, 60 40, 00 40, 00 0 ">
               /polygon>
       /clipPath>
   /defs>
/svg>

3. less/Services/Init/delos.css: set width in il_startup_logo