Okay, the current naming solution is rather accurate and I know why the distances are off from your location. I have attached a screenshot of the app which pulls up all the weather stations in your area (which is available in the app to the right of the location input). You will notice the nearest weather station is Taksony, Pest country.
Since you are inputting a city name into the location field, Weather Underground is picking a weather station for you and sometimes it picks Tokol and sometimes the other which is why your text is changing. Furthermore, the nearest station to your city is in fact in Taksony which is why your city name doesn’t match your actual city name.
To enforce Taksony weather station, use the following location, pws:IDUNAHAR2. This appears to only be 4.8km apart.
I hope this helps clarify things and with this knowledge I am planning on proceeding with using the locality, administrative_level_1 (or country) as the location name on the home page as this helps identify which location’s weather is influencing your OpenSprinkler.
If you want more accurate results, you can setup your own Weather Station and register it with Weather Underground. To make the app only use a specific weather station, you may select it from the map tool or use “pws:ID” where ID is the weather station ID.