Sony Xperia Z3 Compact — Search Issue in Dialer = Contact not returned

Contact is saved also in Google, also in Contacts in Phone.

If i search contact in Contacts, by part of name (characters), contact is returned.

If I search Contact in Dialer/Phone, by characters, contact is not anymore returned.

If i search Contact in Dialer/Phone, by numbers part of mobile number, then contact is returned.

All contacts imported first time in phone are searchable.
All new contacts created (either in Google, either in Phone) have this bad behaviour, when are searched via Dialer.
What am I doing wrong, what can cause this error.

Also, what seems to me strange, is that when i search after Phone app in all apps installes, Phone is three times, Contacts only once. Can this be a cause of the problem...?