Actually as much as I love EDSM, the tags there are simply the person who reported the system and went into the database. They have no relation to the in-game tags and there may be many reasons why something is tagged in game with a different name than on EDSM (for example someone used EDDiscovery during beta, someone has not yet sold their data, etc.).
In EDSM, the "first discovered for EDSM by" name, is just the first person to upload coordinates for the
system to EDSM/EDDN.
A few possible reasons ESDM could have a different name than the game...
The first person to "discover" the system was not sending data to EDSM, so the next person to jump there using EDD or EDMC get's their name shown in EDSM.
The first person to "discover" the system was sending data to EDSM but their ship was destroyed before they sold the data in-game.
The first person to jump into the system sent coordinates to EDSM but did not scan any bodies.
In the game, Bodies are tagged, not systems. In EDSM it's the System, and not the bodies that have a name attached.
So think of the EDSM "discovered by" as an unofficial system tag, since it's related to visiting the system, and not scanning anything.