Most sports I know of (e.g. soccer) will mention the home team first; e.g. if Barcelona plays Real Madrid in Barcelona, the scoreboard will show
Barcelona - Real Madrid 1 - 0
both in the stadium (where the home team is often displayed above the away team) and on television, at one of the edges of the screen.
However, in my (limited) experience of watching NBA, I have often (maybe even always?) seen the away team mentioned first. Most recent example on Dutch television: a summary of Milwaukee Bucks - Golden State Warriors, played in Milwaukee; the scoreboard at the bottom (provided by ESPN) showed GS - MIL, where I expected it would be the other way around. What logic is used to determine which team is mentioned first in the score in NBA games?