In Arabic, the word "زَهْرَۃ" means "flower." From this comes "زَهْرَاء", which is the title of Hazrat Fatimah Al-Zahra (may Allah be pleased with her), meaning "a woman with a radiant white face."
The word "حَرَم" means sacred or revered, and from it comes "حَرَمَیْنْ", referring to the two sacred sanctuaries. If the name is formed as "زَهْرَاءُ حَرَمَیْنْ", it would mean "the flower of the Haramain", which is a meaningful and acceptable combination. However, the reversed form "Haramain Zahra" (حَرَمَیْنْ زَهْرَاء) does not yield a correct meaning in Arabic. Therefore, the name "زَهْرَاءُ حَرَمَیْنْ" may be used.
Allah the Almighty knows best.
Darul Ifta Al-Ikhlas, Karachi.
الصحاح تاج اللغة و صحاح العربية: (674/2)
"والأَزْهَرُ: النَيِّرُ. ويُسَمَّى القمر الازهر ابن السكيت: الازهران: الشمس والقمر. ورجل أزهر، أي أبيض مشرق الوجه، والمرأة زهراء".
لسان العرب: (332/4)
"والمرأَة زَهْرَاءُ؛ وَكُلُّ لَوْنٍ أَبيض كالدُّرَّةِ الزَّهْراءِ، والحُوَار الأَزْهَر. والأَزْهَرُ: الأَبيضُ. والزُّهْرُ: ثلاثُ لَيَالٍ مِنْ أَوّل الشَّهْرِ. والزُّهَرَةُ، بِفَتْحِ الْهَاءِ: هَذَا الْكَوْكَبُ الأَبيض".