Over here in the States we have always called our portable phones : Cellular phones. Or Cell phones for short. I noticed in the UK all y'all call them "Mobiles".
Which does make sense.
Last week I saw a TV commercial for some kind of Cellular service and they said "Mobile".
I heard at a Skeptics' Conference that the phone companies insist on the term "mobile" because they don't want their phones to be associated with things cellular - it reminds people of "cell damage" and the like. I don't know why they're not called "portable" or "pocket" phones. "Mobile" sounds like you push it around on wheels.
(Nerd note: They're called cellular because there is a "cell" of reception around each transmitter, and your phone seamlessly changes from one to another, depending on which has the greatest signal strength.)