Naming Convetion for Edge Connector Fingers

No, there is no standard for board edge connectors, but I would name them after their purpose.

We don't tend to use specific industry standard edge connector schemes such as PCI, PCIE.

For our edge connectors I use:

EDGECON<PITCH>_<FINGERWIDTH X FINGERLENGTH>_<NUMBER-OF-SIDES>X<NUMBER-OF-WAYS>

E.g.

Pitch 2.54 mm, 1.27 mm x 7.50 mm finger, one side only, 10 ways.
EDGECON254_127X750_1X10

Pitch 2.54 mm, 1.27 mm x 7.50 mm finger, two sides, 15 ways.
EDGECON254_127X750_2X15

We use this style of edge connector where we have slots in one board and and edge connector in another and solder the two boards together at right-angles.