Answer:
In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
In principle, it is permissible to keep any name as long as:
1) The name is not prohibited.
2) The name not a common name used by the followers of another religion.
3) The name does not hold a negative meaning.
4) The name does not resemble the name used for the opposite gender.
Some names have been expressly disliked by the messenger of Allah salallahu alaihi wasallam. Other names are makrūh (disliked) due to resemblance with the non-Muslims. The reason behind the resemblance is that names have become a shi῾ār (outstanding feature). One’s religion is easily determined by the name one has. If somebody reads a register or document with the following names Ali, Musa, Fatima and Khadijah for example, he will at once identify them as being Muslims. One’s Islam is identified merely by the name one has.
We have been advised to keep good names. The Prophet salallahu alaihi wasallam said,
“Name your children with the names of the Prophets. The most beloved of names is Abdullah and Abdur Rahmān. The most honest of the names is Hārith and Hammām. The worst of names is Harb and Murrah. Harb means war and Murrah means bitter.
The name Malā’ikah is the plural of malakah. Malakah means an angel and Malā’ikah means angels. The word Malā’ikah has come in the Qur’an approximately 68 times.
It is permissible to keep the name Malā’ikah for a baby girl. It is neither prohibited, nor is it a name used by the non-Muslims and neither does it have a negative meaning.
You may spell the name as:
1) Malaaikah
2) Mala’ikah
3) Malaa’ikah
4) Malaikah
And Allah Ta’āla Knows Best
وفي الموسوعة الفقهية الكويتية
الأَْصْل جَوَازُ التَّسْمِيَةِ بِأَيِّ اسْمٍ إِلاَّ مَا وَرَدَ النَّهْيُ عَنْهُ (ج 11 ص 331 دارالسلاسل)