Hi Pankaj,
There is a content snippet 'Mobile Header' that loads image in the portals by default.
You can update the Header template as suggested by Raghav with your logic to update the image dynamically.
You can
1) create web files with different brand image attached as notes.
2) create html content snippets per brand and refer the image there.
3) Lastly in the Header you can use the liquid if else to include your snippets according to your condition.
{% if user.roles contains 'Role1'%}
{% editable snippets "Brand1" %}
{% elif user.roles contains 'Role2'%}
{% editable snippets "Brand2" %}
{% elif user.roles contains 'Role3'%}
{% editable snippets "Brand3" %}
{% endif %}