IMO, if you name your band after Jesus and Mary, in any particular fashion, then you should be a Christian band. Commenting on the guitar skills of Eddie Van Halen shouldn’t even be mentioned, because it wouldn’t be something a Christian band would care about.
If they’re not a Christian band, and using that name, it’s almost like taking the Lord’s name in vain. Certainly not worth my time.
The Jesus and Mary Chain name was riffed on and gave me quite a chuckle when an NE England super-group was announced. The Joseph and Mary Chain.
This was a Christmas carol charity collaboration of members of the Futureheads and Field Music. They also reunited to do some anniversary shows this past December with proceeds going to homeless and food pantries.