I don't know the name of that bit profile but it's possible the cut is done using just a portion of a bit, e.g the highlighted portion here:
Source: Rockler tambour bit set.
Edit: thanks to the Comment below from Aloysius Defenestrate, the correct bit to use for this is called, obviously enough, a drawer-pull bit. As theorised a portion of the bit is used to form the finger groove as shown.
Source: Drawer Pull Bit on Lee Valley.
In case it's not obvious you could do a very similar cutout using a common dovetail bit. Perhaps not as comfortable but would likely work nearly as well.
Do be aware a cut like this will work better in solid wood than in plywood. Even using excellent all-hardwood ply the router bit will naturally cut the long-grain plies differently to the cross-grain plies so the inside surface may feel rougher than you'd really like. And there may be a tendency for the surface ply to delaminate from the board with extended use.
Also related to the cross-ply structure, to get a good surface on the edge you may want to clamp on a sacrificial board, or, route and then saw to final width to remove the chipped-out edge.
I'm pretty novice and am currently experimenting with my newly purchased router table and am making cut out handles in plywood doors. I'd love to achieve something similar to the attached image.
This kind of cutout would not normally be done on the router table, it's much more common, and generally safer, to use the router with an edge-following fence as supplied with most (all?) routers.