I've seen this happen twice in a row now with group "09a60592-9b6c-4cad-8ab0-8ca2f4108b44" - I keep trying to change the name, but I'm unable to do so.

Thanks for reporting this! 

I wonder if this might partially be because the group renaming UI doesn't make it very clear that you've "saved" a group name change? It's supposed to save when you press enter while focusing the input, but there's not currently a UI indication of this.

Ah! I didn't even realize that this saved it. Maybe it could be made so that a changed text box is saved when it loses focus, and <enter> is just the equivalent of calling .blur() on a text box?

Sure! I think saving on blur would help. Eventually, I think we also will want to make some changes to make name changing itself more discoverable, but this is a good first step. 

The following revision refers to this bug:
  https://chromium.googlesource.com/infra/infra/+/2448f1d8b591bd2d362506ab2e7e05b4ee81e8c3

commit 2448f1d8b591bd2d362506ab2e7e05b4ee81e8c3
Author: Tiff Zhang <zhangtiff@google.com>
Date: Fri Aug 18 23:54:21 2017

SoM: Make group name changes save on focus changes.

Bug:756434
Change-Id: Ia1e307007fa5269f0ba44f3f427ca2e8d6c46f93
Reviewed-on: https://chromium-review.googlesource.com/621594
Reviewed-by: Sean McCullough <seanmccullough@chromium.org>
Commit-Queue: Tiffany Zhang <zhangtiff@chromium.org>

[modify] https://crrev.com/2448f1d8b591bd2d362506ab2e7e05b4ee81e8c3/go/src/infra/appengine/sheriff-o-matic/frontend/elements/som-alert-item/som-alert-item.html
[modify] https://crrev.com/2448f1d8b591bd2d362506ab2e7e05b4ee81e8c3/go/src/infra/appengine/sheriff-o-matic/frontend/elements/som-alert-item/som-alert-item.js

I think the latest change should fix this problem. Feel free to let me know if you still see if though. :) We do also want to improve the UI for alert group naming as well eventually: https://bugs.chromium.org/p/chromium/issues/detail?id=744755

Awesome - thanks for the responsiveness! I'll let you know if I run into the problem again.