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I'm not fully understanding the situation. Please forgive me if this is mundane info but see the following.
Say you want to share contact info with someone. Let me know which step it is that you get to your problem.
1) Open your contacts app
2) Find contact you wish to share
3.a) Long press contact and select share
-or-
3.b) Open contact info and click more>share name card.
4) Select the method you would like to send the name card. Such as text message, email, bluetooth, or similar.
5) Now choose the recipient's number, email, device, or corresponding type of transfer info needed.
6) Compose or simply send the data via the transfer type you choose.
7) Confirm the data was sent / wait for conformation that the data has been transfered.