Subhan is one of the special words in Islam used for proclaiming the glory, purity and supremacy of Allah. Ali bin Abi Talib, may Allah be pleased with him, when he was asked about the meaning of Subhan said: "It is a attribute that Allah has used to describe Himself with," and he didn't say anything more.
When you say Subhan Allah, it means Allah is pure from all defects, flaws, faults and shortcomings, that He is perfect and has all the good attributes and is the source for all good in existence, and separate and opposite of everything that's negative and evil.
The most basic meaning of Subhan is purity from flaws. There is no clear Islamic prohibition on the use of Subhan as a name, but most scholars do not like it to be used as a name and recommend against it, and some scholars say it is not permissible. It is best to keep away from such words since there are so many other good names.