You’re exchanging phone numbers. You have to repeat your phone number and your name and name. Why not simply have the other person scan a QR code that automatically imports your contact info.
I used qrcode-monkey.com but there are several other sites that let you generate QR codes.
Select vcard. Fill out the information you want to share and create the QR code.
Send the QR code image to your phone. Whenever you need to share your contact info, have the person scan the QR code from your phone screen.