This can be done with selections/queries and List or Inspector (Property) assignment.
List:
Select the pins.
Open List panel/dialog. Set: "Edit", "selected objects", from "current component". Include "all types".
Sort by Y1. Select and CTRL+C (copy) the coordinates.
Sort by Name. Paste Y1 coordinates.
Inspector:
Select the pins.
Open Inspector/Properties.
In Y1, enter: Copy(Name, 2, 99)*10
Move pins into desired location(s).
The list method is pretty obvious, just swapping around tables. Synergize with Excel if you need more power (or learn scripting).

The latter expression is the tricky stuff you might not be expecting -- or know very well how to use. Sadly, objects have three different names in Altium, and they don't always make sense. I haven't seen anywhere these are tallied. You read one description in the object dialog or Inspector panel / Property dialog, but that's different from the reference used in an expression. For example, here you can reference an object's name field by "Name", but its designator is "Pin_Designator". But on the Query panel, it's "Name" or "PinDesignator".
Also, note that, to use an expression on a text field, you need to click the "..." and enter it on the Formula tab. Substitution expressions ("{xxx=yyy}") can be entered directly or created in the "..." Batch Replace tab.
Tim