If a gas pump only has one handle, is there residue from different octanes in the pump / am I necessarily getting "my" octane?

There may be a little (less than an ounce or two) residual gas left in the hose. It will not be enough to effect the next customer at all. The hoses are designed to empty when the nozzle clicks off, that is one reason why it takes a couple seconds between selecting your gas and the pump clicking on. It is priming the pump.

If the hose was kept full of gas, there would be no lag when you open the nozzle when you started pumping

@WestRiverrat Thanks so much! How does it empty? Does it get vacuumed or siphoned back out of the hose, somehow?

A tiny amount does stay in the hose, but it is insignificant. You might have a slug of 3 feet of old fuel but the diameter of the hose is only ¾ of an inch so that comes to 18 cubic inches of old fuel. Just about 1% of one gallon. Not worth worrying about. Relax.

Twas easily answered…but, a down-to-earth great question.

There is a little of the gas of another octane left in the hose but it doesn’t matter much. The octane rating on your gas is the minimum octane rating, which may actually be a little higher.
There was a gas station here in town that had octane that was very precisely measured at the pump. (They have 5 or 6 pumps!) My truck required at least 89 octane on a regular pump and I thought I could save a little money by getting gas with the exact octane my engine needed. But I had to get a slightly higher octane for my engine to run properly, so I couldn’t save any money. As it turns out, my engine needed 90 octane! It was better for me to just go back to some other station with the not so precise 89 octane pumps where I could get a actually slightly higher octane for a lesser price.
If I ever went into a station where there was no 89 octane, I would just get 5 gallons of regular (87 octane) and 5 gallons of premium (91 octane).
(The engine knocked on 89 and was overly sluggish on 91. That’s why I had to be so picky.)