Can chords show H instead of B?

In the phone and tablet app, yes. Go to Settings → Songs → Chord notation and choose:

• International (B, Bb), the default,
• Polish (H, B).

On Android you'll find the same choice in the Display sheet in the song view. The setting applies to chords and sheet music on that device only.

When you import songs written in Polish notation (H, fis), WorshipPro converts them, so all your songs are stored the same way.

The browser has no H notation yet. In the song settings in Charts, Notation offers C D E, 1 4 5 and Do Re. The desktop app has no notation setting. If you need H there, vote for it in Ideas.

More about the app in The app for musicians: iPhone, iPad and Android.