I may apply general logic here:
semifinal -not fully final;
semisolid -not fully solid;
semi first-name -not a full first name
I'm not an American so exactly don't know how to shorten names. But let me try...
For instance, your friend's name is Rachel Fishman.
Now here...
Fishman: Last Name
Rachel: First name
Rach: Semi-first name.
Said that, if you are close to Rachel, you don't bother uttering the whole name. What I just said up there...
Hey Rach, bring me beer!
So, if Rachel says, "Let me introduce myself on a semi-first-name basis", I think Rachel is trying to be friendly with the audience/opposite person. Said that, on the very first meeting, Rachel wants to be an amicable person and does not want to get into formalities.
Something like...
Hey, that's okay, call me Rach!
Immediately, the opposite person gets feeling of friendliness.
[In your case, as I said earlier, I'm not sure how to shorten the word 'John' further!]
This is a logical answer, and I'm not sure whether it has something to do with 'culture'. Depending upon comments, I shall improve/delete this. Here, I just tried to help the OP.
This question seems to be asking about two actions. One is someone 'going through' a backpack. The other one is 'going through the things found in a backpack'.
Stop going through my things
fits the second case.
As does the expression you provided:
Stop searching through my stuff
User3169 has provided a highly idiomatic expression:
Stop digging through my things
CopperKettle has provided the useful verb rummage (which is also a noun):
Stop rummaging (through) my backpack
Also, stop messing with my things/stuff is similar, but it is broader in meaning.
You can also say
Get your hands out of my backpack
Leave my stuff alone
Find your own toys to play with
For variety and vocabulary expansion, you might want to be aware of
Stop rifling through my things
but rifle as a verb means to go through something quickly in order to steal something, and we wouldn't generally use that for a toddler.
Note: I have not used a period after any of the italicized examples, because I want to leave open the fact that you can add , toddler's name or something else the end of each one.
Stop messing with my stuff, lovey dovey.
Best Answer
Both sentences are grammatically correct.
There are many different meanings and uses of 'know (of)', but I think the meanings of the sentences above can best be seen as the following two from the (very long list in the) OED:
"There are too many words that I don't know."
That is to say, 'there are many words that I do not understand'.
"There are too many words that I don't know of."
That is to say, 'I am not aware of the existence of a great number of words.'
The difference between the sentences with 'words' is, I think, negligible. However, if you substitute 'words' with 'people', the difference becomes clearer:
"There are too many people that I don't know."
Which could mean that you don't know the people (at, for example, an event) personally.
"There are too many people that I don't know of."
Which could mean that you haven't even heard (a lot) about many people, and you might be oblivious to their existence.
The first use of 'know' can actually also mean 'be aware of', but it is made more explicit with 'know of'.