Alaikumassalam wa rahmatullah,
Shaheen is a type of bird of prey, the Peregrine Falcon. The word is used in Arabic and the origin is old Persian. In Farsi it could also mean "like a king". It is the name of a scholar of hadith, Ibn Shaheen. The word doesn't have an Islamic meaning, but it is acceptable to use it.
Shadhin , pronounced (SHA)rd + (TH)is + cl(EAN) is the plural of shaadh, which means exceptional, eccentric, unique.
Shadhin, spelled and pronounced the same as above, is also a rare name for girls in Arabic with unclear origin. It is not the plural of shaadh, but it might be related to it, since Arabs often add an extra "an" to the end of a word to form a name (even though it is not grammatically meaningful, it just sounds nice), and the meaning might be "unique", "special".
If you live in an Arab country I don't recommend using it due to the double meaning (unique, deviant). But if you live in a non-Arab country then there are no issues with it. It is not used in the Quran directly or indirectly, but since the meaning is good, you may use it.
Shazeen, pronounced as (SH)iny + h(U)mble + (Z)oom + cl(EAN), , means active in Arabic (not lazy or lethargic). This word is not used in the Quran either directly or indirectly, but since the meaning is acceptable you can use it.
Rakeem is another spelling of Raqeem. Click on the name to view its details.
For Sarim please look at: Sarim