A Dutch bishop suggested that Christians start referring to God as Allah to improve relations with our Muslim brothers and sisters.
Theologically, I’m not sure if there are any big things in the way of this. God has given us many different names for him; Allah is one that we didn’t receive in our tradition, but I don’t know if that means anything.
Personally, I would rather not adopt the term used by another religion, even for the same God, until I had a better understanding of what the name of God means to them.