What does 'Christian' mean in a Muslim context?

A rather arcane (1938) document has recently come to my attention. It is the Riggs Report from the Near East Christian Council (NECC) meeting in Beirut back in the day. They were trying to figure out why so few Muslims were converting. (Though most people are interested in how this relates or does not relate to the whole Insider Movement debate, several other interesting points are made.)

Anyway, here is a section I thought was quite interesting and wanted to share with you:

[...] the name Christian, in the Near East, has almost exclusively a racial, political and social group-connotation, and does not suggest either a new way of life nor a spiritual rebirth within. If a group of believers is to grow up as indigenous and not alien, they cannot take on themselves that particular name. Some other terminology must be developed.

So what do you think? Can we toss out the word 'Christian' because it is misunderstood by Muslims? If so, what should we use in its stead?

The whole document is HERE, if you are interested in reading it. He followed this up with a 1941 article in Moslem World on the topic, but to my knowledge that is not available anywhere on the internet.