How do you teleport multiple entites forward at once in 1.13?

Solution 1:

It took a bit of testing and thinking to figure this out. Since using @s didn't work, I came up with a not very pretty, but working command:

/execute at @e[name="Name"] run tp @e[name="Name",distance=0] ~1 ~ ~

This is the command that you had, but with the distance tag added. Now, every entity with that name will teleport only itself instead of every other entity with the same name.

Solution 2:

You used @e twice, so you split up the command between all entities twice. You teleported every entity to every entity. This throws all your poor animals around the entire world many times in less than a second until they finally land at whatever spot happens to be the last one.

The solution is indeed @s, but that only works properly if "myself" actually means the entities you want, which you can change with /execute as:

/execute as @e[name="Name"] at @s run teleport ~1 ~ ~