According to Acura's product planning graphic that leaked last year Acura will continue to offer a compact sedan, but it probably won't be called ILX. The planning graphic noted "new compact sedan/type S" So whatever it is will probably be based on the new civic (the rumor being that if the civic hatch gets it's own platform, the new acura will use this platform as well, but just a rumor at this point.)
The ILX is based off of the 8th/9th gen civic platform, and uses the old 2.4L engine from the 9th gen Si. But there is a new compact sport sedan coming along with an accompanied Type S variant, according to Acura's planning which went up to 2023 I believe. Now that they've got their core models out of the way, they just need to finish introducing the Type S for the TLX and MDX and their next reveal should be this new compact sedan.
As for a name? No idea... it may end up resurrecting the RSX name for the new generation. Safe to assume it'll use a version of the 11th gen Si powerplant for base models and the 2.0T for it's Type S variant. Expect it to rise in price significantly from the current car which starts lower than a civic touring currently. Assuming it gets a price bump equal to the TLX, expect pricing to start in the low $30k range with the Type S coming in just under $40k most likely.