In Tehilim 93:1
יְהֹוָה מָלָךְ גֵּאוּת לָבֵשׁ לָבֵשׁ
which the Igeret HaRamban brings as a proof that one who is proud dons the royal clothing of God, thereby "rebelling against His Kingdom".
In this context, what does it mean that God dons pride? Pride for what?
It appears that you may be misinterpreting the intent of the reference to "pride" as shown in the translation of the Igeres HaRamban.
Tehillim - Psalms - Chapter 93
יְהֹוָה מָלָךְ גֵּאוּת לָבֵשׁ לָבֵשׁ יְהֹוָה עֹז הִתְאַזָּר אַף תִּכּוֹן תֵּבֵל בַּל תִּמּוֹט
The Lord has reigned; He has attired Himself with majesty; yea the Lord has attired Himself, He has girded Himself with might. The world also is established that it cannot be moved.
The word that you translate as pride is translated here as majesty. That is, since Hashem is the ruler, He is the one who "dons majesty". Thus one who attempts to exhibit pride or majesty is stating that he is the ruler and takes precedence. The analogy is to one who attempts to wear the robes (or crown) of the king. This could, in modern times, be like wearing judicial robes in a court room. Only the actual judge is allowed to wear judicial robes. It would be like the idiom of "donning judgement".
I think that this is the way the Ramban is expressing the idea in the Igeret. The translator used "pride" in the way that I used Judgement above or Majesty in the Chabad translation.
The Ramban means that only Hashem is deserving of the title of "Proud" because He is the ultimate cause of everything in this world. For example, if a fireman saves someone from a burning building, the fireman would be wrong for feeling proud about his accomplishment because it is only Hashem who gave him the physical capabilities as well as intellectual capabilities to make the rescue. Hashem also created the scenario that allowed him to make the rescue and was overseeing the rescue and controlling it from beginning to end. This concept applies to everything in life - whether you passed your CPA test, finished a Mesechta, or drove from Brooklyn to Lakewood. For this reason someone who feels pride about an accomplishment is actually limiting in sone sense his recognition of Hashem being in full control of everything.
The sefer Hachinuch explains in numerous places that the attributes of G-d in the words of Tora are "כלפי המקבלים". This is a language which makes sense for the listener or the reader. גאות is eight, altitude, a gap between a man and G-d.
Similarly if we admire someone, we are impressed by the gap. If someone feels a gap between himself, he take for himself the feeling of gap he needs to feel for hashem.
