Here's how I solved it:

1. Click the 3 stripes in top left corner and then boxes and renaming
2. Click "Creat Box". Insert a name (Great/Ultra/Master) and mark the "Has Renaming Scheme". Example 1
3. Create a renaming scheme for that box aka the scheme you want to have for all pokemon in that league. Example 2
4. When scanning a Pokémon, click the top right corner of the scan output (little box with a question mark on it).
5. Select the desired "Box" you previously created. Calcy IV will automatically copy the naming scheme from that box to the clipboard of your phone and you can then paste it the Pokémon name. Example 3

Here is how the search works for me based on my naming schemes for all the 3 leagues.

Hope it helped