They have a girl's name for a chess clock?
Aurora Chess Clock for Android

Your app is excellent! It's attractive, easy to operate, and covers any time scenario I would need.
The only thing that confuses me is minor:
What is the best way to resume the countdown after pausing?
What seems to work best is to quickly "press the lever" for each of the players. Usually when I do that the move counter correctly does not change, although the player not pausing could lose a few tenths of a second.

Yes, that's the only way so far. Thank you for your note, I will add resume function for pause button in the next update.

Version 1.3 is available
- pause button works as resume
- added a button to adjust the current time on pause
- added reset button on main screen
- sound and interface settings as well as default time settings are now stored
- show milliseconds option works for 10 min or less time control
- preset settings are available in free mode (purchase only removes ad banner)
- you can choose 1, 2 or 4 ticks per second for clock ticking (4 ticks may be too fast for slow smartphones, please, consider using 1 or 2 on that case)
If you like the application please share the link: https://www.facebook.com/AuroraBorealisDraughts/posts/1601881973203397
I will appreciate feedback, comments and suggestions too.

Version 1.5 is available:
Buttons and settings window are optimized for different resolutions
Clock counts and shows moves not only in countdown modes.
In simple delay mode clock shows left seconds in the upper right corner
Added an option to save the state: the program saves its state on unexpected shutdown (low battery, process unloaded from memory by Android being in background, etc.) and on next startup will restore its state. This option may affect performance
so is not recommended for slow devices.
Available in Google Play, iOS version has been finished also, will be available in AppStore soon.

It's cute, but there looks to be close to 100 chess clock apps in the Google Play Store, none of which are legal to use in tournaments.
I guess it's difficult for me to see how much of a market there is for this type of app.

I never thought about big market, for me it was just my first application to test programming skills on Android. So far it earned less than 100$ (In-App purchases plus ads) so I wouldn't say it was very commercial program
But for example, clock app from chess.com in Google Play has 1 to 5 millions downloads in 3,5 years, some apps have 100 to 500 thousands. So i assume players do use these apps.
For sure, they intended mostly for amateur players, to play a couple of games with your pal, few of us have real chess clock. But I see no reason why woudn't some chess club use an app for local tournament, instead of expensive real clocks. If it covers needed time scenarios (and here applications should be even more flexible). As a matter of fact, some time ago I saw a video in Facebook from draughts tournament somewhere in the middle Asia (Iran, or Kuwait maybe) and they used smartphones with Aurora Clock on some tables. It was funny. Maybe there were more players than they were expected, or had some clocks broken.

By the way, Aurora Clock is already available in AppStore:
https://itunes.apple.com/us/app/aurora-chess-clock/id1349971561
I've made it paid there, just to check and test different ways of distribution.
Please. check this app out:
https://play.google.com/store/apps/details?id=com.AuroraClock
I tried to make simple but powerful and universal application.
If missed anything important - please let me know.