playstation series emulator names

[Made in China]

PS1:
ePSXe = emulator + PSX + emulator.
*PCSX = PC + PSX => PCSX-R = PCSX Reloaded.

PS2:
*PCSX2 = PCSX + 2. The X doesn't really belong but is kept due to branding - the same team created both emulators.

PSP:
-JPCSP = Java + PCSX + PSP.
PPSSPP = PSP + PSP.

PS3:
-RPSC3 = Recompiler + PSCX + PS3.

As you can see, most of the emulators share the "PCSX" name due to mostly historic reasons, and using the "brand" to promote new emulators. As far as I know, for an example, there is no direct connection between PCSX/PCSX2 and JPCSP/RPCS3, though each of those groups has mostly the same team members.
PPSSPP is an outlier to that trend, and ePSXe was an original competitor - so it didn't really have a trend to follow.

The more you know.