I later learned that the syntax for tp has changed. When using relative positioning it is relative to the executor, not the target. This command would teleport the armor stand named 1 to me, the executor. My thought would be to have the command ran off the armor stand. Although this produced the same outcome:
/execute as @e[type=armor_stand,name=1] run tp @s ~ ~ ~ facing entity @e[limit=1,type=armor_stand,tag=1]
What command can I use to face the armor stand towards the other one without teleporting it to me?