Answer
(Fatwa: 138/101/D=1434)
Shaikh means: elder, old age.
Altaf means: friendliness, kindness.
Hussain means: the grandchild of the holy Prophet Muhammad (صلى الله عليه وسلم).
Abdur Rahman means: the slave of Rahman.
Halima Sadiya: the blessed woman who breastfed the holy Prophet Muhammad (صلى الله عليه وسلم) in childhood. The holy Prophet Muhammad (صلى الله عليه وسلم) passed the period of infancy in her lap.
Halima means: lenient, mild.
Sadiya means: fortunate.
In the names of Sahaba, Sahabiyat and elders, instead of literal meaning, it is enough that the name belongs to so and so Sahaba and Sahabiyat and hence it is blessed and good to keep.
Abdur Rahman has been mentioned in hadith to be a favourite name. Thus Halima Sadiya is also good one. You may keep the name Altaf Hossain as well. If you keep only Hossain then too it is very good, the holy Prophet Muhammad (صلى الله عليه وسلم) liked the name for his grandchild.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband