The word Emmanuel is a Hebrew name, and its interpretation means “God with us”.  The Hebrews often named their children with names that made reference to God and His attributes.  For example, Elijah's name means "God is Yahweh", and Samuel's name means "his name is God".

Just because God was with Jesus, and hence Jesus was among us, does not make Jesus into Yahweh.  When Jesus raised back to life the widow’s son, the people who saw the miracle “glorified God, saying, That a great prophet is risen up among us; and, That God hath visited his people.” (Luke 7:16).  Note that the people who witnessed this miracle did not believe that Jesus was God, for there is no indication that they bowed down and worshipped Jesus.  The people referred to Jesus as "a prophet", and not a god.  Rather, they understood that God used Jesus to perform the miracle.  In this sense “God hath visited his people”.  In this sense God was with us (or them, in this case).  God was working THROUGH Jesus, and this is how Jesus can be “God with us” without Jesus being confused as God the Almighty.