Block devices sda, sdb, sdc. What comes after sdz?

My block devices are named sda, sdb and so on.

What happens when I get to sdz? Is the next one going to be called sdaa?

Yes. The kernel will continue to assign names in the form of sdaa, sdab and so on. There may be a bug preventing it from going beyond sdzzz, but in theory, it's going to continue forever (that is up to 18278 due to data type limitations).

_{my thanks to Rinzwind for providing the links}

After sda➡sdz comes sdaa➡sdaz, etc.

The first link in the accepted answer (from 2011) is broken. Here is a new link (also from 2011) containing a good write-up: How are Linux drives named beyond drive 26?.

To summarize the main point in the link (slightly revised and reformatted):

Drive # - Name
1       - sda
26      - sdz
27      - sdaa
28      - sdab
52      - sdaz
53      - sdba
54      - sdbb
702     - sdzz
703     - sdaaa
704     - sdaab
18278   - sdzzz

Needless to say Linux is well positioned for expansion of drives.