After further reflection, some of the fine details in my comment above may be off. I vaguely remember MySQL having a single server-wide (I believe?) configurable charset option before MySQL 4.1, so it's likely the MySQL C client library API gained mysql_real_escape_string earlier than 4.1.
Anyway though the broad point remains -- PHP didn't pick the "real_" naming, MySQL did; and the reason for MySQL's API there makes more sense in the historical context of expanding charset support, and needing a different C function signature to accept a connection arg.
And fwiw I do agree that "real" is a rather poor choice for this sort of API naming, but I assume the MySQL folks just went with that to avoid an excessively-long function name... also the developers of MySQL weren't native English speakers. Anyway, hindsight is 20/20 and all that.