This has always bothered me, that there are Jewish believers who prefer to call themselves by another name. I do like the term Messianic, but when people use it to divide themselves from the Church it really makes me disdain the term. The apostles taught that there is no difference between the Jew and Gentile in Christ, such a division doesn't exist. We are one people, of one body, of one Lord, with one baptism, indwelled with one Spirit, and one inheritance.
But, Dave, I will consider what you have brought up. How about the first letter of Peter that was written to...
"...those who are the elect exiles of the Dispersion..." - (v. 1)
He says in that same book,
"Yet, if anyone suffers as a Christian, let him not be ashamed, but let him glorify God in that name." - (v. 4:16)
What are your thoughts?