There is also b6.
1. d4 nf6 2. e3?!

Why are you suggesting that 2.e3 is a dubious move? It seems perfectly reasonable and can lead into some English variations, some Queen's Gambit variations, the Nimzo-Larsen, or other openings as well as possibly being independent
My guess would be that white's opting for a Stonewall or a colle as blueemu mentioned. nothing a KID can't handle! (why not?)
well from various opening databases it appears white scores significantly less than black---- by the 2nd move!

I actually misread the moves, 2.e3 is typical of a Colle setup with Bd3 and is certainly not dubious. I thought you were talking about 1.Nf3 and 2.e3 which could lead to the openings I listed. Black cannot hope to get an advantage out of a major opening unless White screws up, and 2.e3 is not a screw-up.
In my rating range ( quite low ) , this is the second-most often played variant by my opponents , after 2.c4 . So for the sake of my own handwritten lists I was looking for a name , but could´t find any , even on numerous famous chess sites .
But maybe someone has already given a suggestion in a book , like " White Stonewall Preparation " , " Colle vs Indian " etc ... ?
My main response has been 2...d5 , where my opponents go often into an almost Colle set-up . In the future I plan maybe to try 2...c5 and see what happens .

always the same story...
Depends on what u play on "big lines".
Giving advice with KI set up, Grunfeld set up, etc... is a bit useless if u play Nimzo indian...

I dont use this opening a lot
It's good that you don't use it a lot. You have just blundered away your knight on move 3.
I play 1.d4 2.e3 and Nf3... after discovering David Rudel's work on 9.b4!? Colle Koltanowski against Black's Nc6 line (playing a true Semi-Slav as White with a move, also got a seal of approval from Milos Pavlovic)
That stated ... I play the Semi-Classical var against the KID. (at my level i.e. 1800+ Lichess) the KID doesn't present as many challenges as the Nc6 main line of the Colle Koltanowski.
I have three lines
8.b4 & 9.Bb2
6.b3 & 7.Bb2
and 8. dxe5 w/ a delayed e4
At my level.... I catch more than a few KID players off guard playing the Semi-Classical. There is not a lot of theory on it published, and seems to be ignored by most KID theorist.
seen this happen in couple of games... do you guys prefer
g6, e6, d5, or even c5?