I checked a Greek concordance (for the NT) on the use of "brother(s)" (Greek adelphos, Strong's # 80). Curiously enough, of the 343 uses of the word in the NT there aren't any examples of a first person address, "brother so-and-so," except one: Acts 9:17 (and Acts 22:13, which is Paul's retelling of what Ananias said in 9:17).
But the example in Acts 9:17 may have been Ananias' timid/careful approach to someone (Saul) that he knew to be a cruel persecutor (compare Acts 9:10-17). So it is a sort of one-off.
Fellow Christians, fellow countrymen and family are otherwise all spoken of, or addressed, on various occasions as "brother(s)" without any name added.
The norm for direct address to an individual was to speak to them using their name ("first name" in modern lingo).
I also admit to feeling odd being referred to in public (away from the KH) as "Brother Last-name." It makes me feel like people will think I live in a monastery. Yet it is so ingrained. There is a sister who recently started working where I work, She started calling me "Brother Last-name" (at work) but I told her just call me "Bobcat." Now she doesn't call me anything. She talks to me, but she doesn't address me in any way. It is almost like she isn't able to refer to me in any way except "Brother Last-name."
Bobcat