In fact, the call is being transferred from one phone to another, but we do understand that it means we are trying to connect two people on the call. One other way to say "transfer" would be "Please hold while I connect you to _______" But in North America, we usually say "transfer/transfer the call".

"Transfer someone to" usually means transfering the call from one phone to a different phone. Often "connection someone with" means the same thing. "Pass someone to" or "give someone to" are more generic; it could be calling someone to the same phone, or it could be asking someone to pick up a different phone on the same line just as easily as it could be to transfer the call to a different phone.

The most normal ways that would be said in English would be. "One moment, I'll get him/her" "One moment, he'll/she'll be right here" "Just a sec, he's/she's right here" - Informal "I'll pass you over (to him/her)" - Informal "Hang on while I get him/her for you" - Informal "One moment please." "Please hold (on) while I get him/her for you" Normally, "I'm gonna pass you" would not be used. You'd more often hear. "I'll pass". In fact 'gonna' is very colloquial and is not used often even between close friends. It has a connotation of laziness or roughness.