This has just came up in one of my games. In the end it remained unresolved before the game ended in resignation. However upon reviewing my game I found this to be rather tricky. Hard to avoid the KO.
Does this have a name?

Click Here To Show Diagram Code

[go]$$c
$$.......X..|
$$.......X..|
$$......XX..|
$$......XW..|
$$....OOXW..|
$$....OBWW.W|
$$.OOOOBBBW.|
$$........B.|
$$----------[/go]

I'm asking about the marked formation. I just made up the rest. (Also, this is my first diagram ever - if I remember right.)

If white plays first, I think they can win:

Click Here To Show Diagram Code

[go]$$W
$$.......X..|
$$.......X..|
$$......XX..|
$$......XO..|
$$....OOXO..|
$$....OXOO1O|
$$.OOOOXXXO2|
$$....53.4X.|
$$----------[/go]

In this variation white lives with double ko:

Click Here To Show Diagram Code

[go]$$W
$$.......X..|
$$.......X..|
$$......XX..|
$$......XO..|
$$....OOXO..|
$$....OXOO1O|
$$.OOOOXXXO.|
$$...52.43X.|
$$----------[/go]

If black plays first, I think a direct ko white takes first is the best result:

Click Here To Show Diagram Code

[go]$$B
$$.......X..|
$$.......X..|
$$......XX..|
$$......XO13|
$$....OOXO24|
$$....OXOO.O|
$$.OOOOXXXO5|
$$........X.|
$$----------[/go]

If it’s White’s turn, wouldn’t then S5 do it?

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I think after 1 below "a" and "b" are miai.

Click Here To Show Diagram Code

[go]$$W
$$.......X..|
$$.......X..|
$$......XX..|
$$......XW..|
$$....OOXW..|
$$....OBWWaW|
$$.OOOOBBBWb|
$$.....1..B.|
$$----------[/go]

Edit:
If black plays first it looks trickier - I think the below throw-in ko might be strongest?

Click Here To Show Diagram Code

[go]$$B
$$.......X..|
$$.......X..|
$$......XX.3|
$$......XW1.|
$$....OOXW24|
$$....OBWW.W|
$$.OOOOBBBW5|
$$........B.|
$$----------[/go]

Actually, seems like the below is also a throw-in ko, so it's pretty much the same?

Click Here To Show Diagram Code

[go]$$B
$$.......X..|
$$.......X..|
$$......XX4.|
$$......XW13|
$$....OOXW2.|
$$....OBWW.W|
$$.OOOOBBBW5|
$$........B.|
$$----------[/go]

Click Here To Show Diagram Code

[go]$$W
$$.......X..|
$$.......X..|
$$......XX..|
$$......XW..|
$$....OOXW..|
$$....OBWW.W|
$$.OOOOBBBW1|
$$........B.|
$$----------[/go]

Doesn't this kill the ko option? One eye beats no eye.

Yeah - the same reason why the first line hane works too. Is this one cleaner in terms of threats or is the first line hane cleaner?