Mu'tasim

I tried to find which affix or lexeme meant faithful and which meant god only to find out that the translation is wrong. [noted -ed]

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Here is what an Arabic expert says on this matter (and it goes hand in hand with what wikipedia threw me when I searched on my own):

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Mu'tasim is a subject name, or the doer of the verb i'itasama:
Now. اعتصم, which is the root of the verb means "to have refuge in"
اعتصم بالصمت i'itasama be'ssamt = means had refuge in silence, ie kept silent.
So mu'tasim means the person who is having refuge in, and for religious and cultural context in general, it is understood "to have refuge in God" which means simply to abide by the God's rules and be faithful.
المعتضم بالله, Al-Mutasim Billah, is a proper name and taken for one word which was the name of some Muslim Caliph in the Middle Ages.
Al-Mu'tasim Billah can be subdivided into:
Al ال Mutasim معتصم Bi بـ Allah الله
Al (means the) Mutasim (having refuge) bi (in or with) al-lah (the God)
So, all in all it means (the one who has refuge in God)
However, nowadays Muslims name the proper name (Mutasim) for short which is understood to be (Almutasim Billah) and in rare cases they name their kids that full proper name.