Is there a nominalized form of "to give"?
There are three; give, gift and completely separately, give.
Of the sense of the verb meaning "to transfer to another person, to donate" we have the noun give referring to the actual thing donated from Old English until around the early 14th century then dying out. We also have it used for the act of giving from the late 13th until the early 14th:
The spellings ȝefe, ȝiftes and yeue are found for this sense.
But then that died out with gift becoming the form used for the act of giving (as well as for the thing given, in which use it is currently much more common). This continued into use until the 19th century:
Language always makes gift of its best wealth to a great poet. — Henry Reed, Lectures on English literature, a1854.
Wouldn't have'em at a gift. — Thomas Hughes, Tom Brown's school days, 1857
The idiom "in one's gift" used this sense of the word to mean "in one's power or right of giving":
The minor appointive offices which lie in his own gift. — James Bryce, The American Commonwealth, 1888.
I'd recognise that sense today, though consider it archaic. While I imagine the straight use of the word in that sense is largely obsolete today (though the OED doesn't list it as such).
Separately from that, the verb give acquired the sense of "yield" which give us yet another separate noun sense of give, the fact of yielding or the degree of doing so:
They began levelling the pitch at 8 a.m. this morning and if the weather stays fine we should have a fair surface with some give in it. The Times (London) 1970.
This sense is still very much current.
The others not so much, and as a matter of current-day word choice I'd suggest donation or perhaps giving, but as a question about morphological nominalisation the answer is give, and also gift.