Minecraft – How to hide functions from the autofill menu in Minecraft Bedrock Edition

This is not possible. Autocomplete always shows all options (except where there are nearly infinitely many, like in a scoreboard name) and functions don't have a permission system by themselves.

The best you can do is to put all functions that users should execute into one namespace and all automatically called functions into another, that way you can enter /function run: and autocomplete from there.

I think it would be easier to execute players who have thrown a specific type of egg instead of executing the egg itself. Since I don't know Bedrock Edition commands, I'll use PC commands and hopefully you can edit them to your liking, or someone else can edit them in this answer.

Add an objective that tracks players who throw eggs:

/scoreboard objectives add egg minecaft.used:minecraft.egg

Then have these commands running in a repeating chain:

tp @a[tag=egg,scores={egg=1}] <write your spawnpoint coordinates here>
tag @a remove egg
tag @a[nbt={SelectedItem:{id:"minecraft:egg",tag:{display:{Name:"\"Spawnpoint\""}}}}] add egg
scoreboard players reset @a egg

What this does is:

• Teleports all players who have thrown an egg with the egg tag to the spawnpoint.
• Removes the egg tag of all players, then adds it for those who are holding the specific egg. In the next tick, if they had held this egg before throwing it, they will be tped. The reason why I added the tag after the tp command is because they wouldn't have had the egg anymore so tagging them would have been impossible.
• Resets their egg score.

That system was for 1.13 commands. If you're using 1.12, use these commands instead.

tp @a[tag=egg,score_egg_min=1] <write your spawnpoint coordinates here>
tag @a remove egg
tag @a add egg {SelectedItem:{id:"minecraft:egg",tag:{display:{Name:"Spawnpoint"}}}}
scoreboard players reset @a egg