The files "ui_*.h" are generated files and not anything that Qt Creator has anything to do with. Qt Creator preserves the case of file names it does have something to do with perfectly well here.
It's not clear exactly which include files you might be talking about. If you have include files specified for Promoted Widgets then uic preserves the case of the include file name you gave it in Designer. For example, this UI file excerpt:
<customwidgets>
<customwidget>
<class>FancyPushButton</class>
<extends>QPushButton</extends>
<header>fancyPushButton.h</header>
</customwidget>
<customwidget>
<class>UglyPushButton</class>
<extends>QPushButton</extends>
<header>Uglypushbutton.h</header>
</customwidget>
</customwidgets>
<customwidgets>
<customwidget>
<class>FancyPushButton</class>
<extends>QPushButton</extends>
<header>fancyPushButton.h</header>
</customwidget>
<customwidget>
<class>UglyPushButton</class>
<extends>QPushButton</extends>
<header>Uglypushbutton.h</header>
</customwidget>
</customwidgets>
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translates through uic to this C++ code:
#ifndef UI_UNTITLED_H
#define UI_UNTITLED_H
...
#include "Uglypushbutton.h"
#include "fancyPushButton.h"
#ifndef UI_UNTITLED_H
#define UI_UNTITLED_H
...
#include "Uglypushbutton.h"
#include "fancyPushButton.h"
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Notice that case is preserved.
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