In Islam is the same God worshipped as the Christians worship? In other words, is Allah and Jehovah just different names for the same God?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is not possible to say that Muslims and Christians worship the same God.  Because the Christians do not worship Allah, The One, who is worshipped by Muslims.  They worship Jesus (), and claim that he is God (Allah).  Some of them claim that he is son of God – Allah is High Above what they say – that is why Allah Said about them that they are unbelievers (Kufar) by Saying: {Surely, in disbelief are they who say that Allâh is the Messiah, son of Maryam (Mary)….}[5:17]  Allah further Says (interpretation of meaning): {Surely, disbelievers are those who said: "Allâh is the third of the three (in a Trinity)."….}[5:73].

Allah knows best.