Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
Is a woman`s nephew by suckling considered a Mahram( i.e. unmarriageable)who is permitted to accompany her to Hajj?
All that is prohibited by lineage is prohibited by suckling, and a nephew by suckling is a Mahram like a nephew by lineage ;therefore, it is permissible for him to be a Mahram for his aunt in Hajj and Umrah.
If a disposable water bottle has the logo (Al-Aziz Water Shop) ,is it allowed to throw it away considering that (Al-Aziz) is one of Allah`s beautiful names?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
You can remove some of the letters so that the word isn`t read as (Al-Aziz). And Allah The Almighty Knows Best.
I work for a company whose manager refuses to allow employees to leave during work hours. Do I incur sin if I secretly went out to join the congregation at the Masjid? Is doing so considered a breach of trust?
Praise be to the Lord of the Worlds.
We recommend that you pray at work to encourage your colleagues to follow suit, because whoever guides to good has the like of the reward of the person who actually does it. And Allah The Almighty Knows Best.