How do I make an entity move to the side?

You have to start by fixing your command, the target selector uses [ ] and NOT { }, and the armor stand is internally called armor_stand, or minecraft:armor_stand to be more precise, and NOT Armour_Stand:

/tp @e[type=minecraft:armor_stand,name=Player] ~ ~ ~-1

Now, as you already said, the armor stand teleports relative to the command block, this happens, because the command is executed as the command block, to fix this you would tell the command to execute as the armor stands instead:

/execute as @e[type=minecraft:armor_stand,name=Player] run tp ~ ~ ~-1

Now you run this command and... it still fails.

This happens, because the command now executes AS the armor stands, but still at the coordinates of the command block. To fix this you would also need to execute at the coordinatees of the armor stands:

/execute as @e[type=minecraft:armor_stand,name=Player] at @s run tp ~ ~ ~-1