It looks to me like a regular Slav Defense, but with the c1 bishop inside the pawn chain, instead of developed outside the pawn chain on f4 or g5. Luckily for you, literally my most recent YouTube video is explaining the reason behind this decision in similar situations 
I don't think this opening idea has a different name though. I'd just call it a Slav Defense where white chooses to not develop the c1 bishop outside the pawn chain.
The official name for the line is the Quiet Slav.
Firouzja-Nepo R7 Sinquefield Cup Quiet Slav Analysis by Mohammedreza Firouzja
Whenever I renovate my d4 repertoire, this will be my d4 prep. I used to play primarily the Slav and Semi-Slav as Black and Traditional QGD as White, but since I started playing Nimzo/Bogo as Black and the Catalan as White, there's no added value in learning multiple sharp, highly theoretical lines in the Slav and Semi-Slav as White so I know how to play them as Black, so I'll be reducing my prep to the Quiet Slav and possibly the Carlsen 3. e3!? on occasion with transposition possibilities to the more positional Semi-Slav variations: the Stoltz and Chigorin variations.
Is the e3 Slav? ECO D12
According to Chessgames.com database this gets a lot of GM love Stats are something like
36.3% Wins for white 39.9% draws 23.8% wins for Black. The opening looks to have a decent pedigree... with Ruben Fine playing it back in the late 1930s to GM Dreev essaying this a lot in the last decade. So far in OTB play and internet... (at my level) I have had pretty good results. I play the Colle and this opening (I think it's called e3 Slav IDK... ??? ) seems to post up the Anti-Colle player. A lot of options for white...
Anyone know what this is called ? Is it the e3 Slav, or its called something else... ?