KGT p. 101. When taking a table's order, the jabwI' neither write anythingdown nor enters data into a computer. It is considered the duty of the jabwI'to remember (qaw) the choices and to bring the correct food, and servers tendto be quite skilled at this. On the rare occasion when the jabwI' has remembered incorrectly (qawHa'), the patron may reject (lajQo') the dish. If the patron rejects a dish that the server believes has been properlyremembered, however, the misunderstanding could develop into minor combat. Formost of the other diners in the restaurant, this is regarded as an exhilaratingdiversion.Antonyms: lIj

Using qaw "remember" seems to work in your example of Dochmey qawbogh "things he remembers/remembered."

But I agree — it's a little awkward. And what one remembers should probably be described as something better or descriptive than simply "things."

We've got qawHaq "memory banks." Maltz didn't know what Haq in this word was. (He said it has nothing to do with surgery — that's just a coincidence.)  But qaw, he said, is a perfectly fine noun meaning "memory" in the sense of the ability to remember or the power of recall.  It does not refer to specific memories or recollections. That's a different word: wov'on.

It's more common to hear wov'on qaw "he/she remembers a memory" than wov'on ghaj "he/she has a memory," though the colloquial (English) translation of the former would be "he/she has a memory."  Someone who remembers a lot of stuff or who can easily remember things (like dates or lines of a play) may be said to have a qaw pov "excellent memory."

qawHa'   remember incorrectly (v)
lIj              forget (v)
wov'on      memory (recollection)