How to teleport a villager with a pseudo NBT tag?

Solution 1:

First of all, those are called "pseudo tags".

Secondly, there is an easy way to accomplish this - tags.

By tags I don't mean NBT tags, but the tags you add on to an entity with the /tag command. Simply tag the villager with something and teleport entities of that specific tag.

E.g. /tag @e[type=villager,sort=nearest,limit=1] foo /tp @e[tag=foo] to somewhere

Or

You can summon an entity with a default tag as well

/summon villager ~ ~ ~ {Tags:["foo"]}

Always look for easier ways to solve a problem.

By the way, I tried out your original command and it seems like your original summon command would not summon a villager with the pseudo tag. Even using /data merge {Fake:1b} won't do the job. If I were you I would not waste time on this. NBT is simply something that determines entities' properties and there are other, much easier approaches to your problem.