Zagreb & Agram

Is it possible that Zagreb and its German name Agram derive from the
same root?
I am not a linguist, but it seems to me that both words derive from
something like 'Zagramb'.
First mention of Zagreb is in form 'Zagrab' (Zagrabia), so it looks
that borrowing took place quite early.
Usual explanation of Zagreb name is from slavic 'za' (behind) + some
word derived from ie. root *ghrebh (scratch, dig, claw).

I would appreciate any comments.