Name of the clutch part?

When you move it slightly forward-backward, it has free moving (empty space) around the circled yellow plastic pin about 2-3 mm. Should it be like that, or what should I do?

I came to this question because of a problem of sudden stalling (sometimes on road holes, sometimes when gears shifting, sometimes accelerating, and after lot of inspections (injectors, fuel pump, inertia switch, relays, ignition pack) noticed that an armor hose carrying lot of cables is touching to this part. When inspected, the hose was even damaged on the touching bottom (luckily wires were all okay). After fixing the hose upward with a plastic tie, the problem did not appear in the next few driving's.

Thanks for your patience and time.