So there's an anon on the wiki I'm admin on with a high number of good contributions. When they started to create an overdue article, I invited them (via comment) to create a user account, mentioning the attribution of their work to their "name".
After they finished that page, an account was created, and simultaneously a user page for the IP address they used since August 6, with the profile text "aka USERNAME".
But, okay, is there some policy for what to do with this anon profile? Can it stay? Shall I simply delete it? (I'm asking especially for a policy to be able to give an official link as explanation to the user why I deleted that page.)
There is no FANDOM site-wide policy (as far as I'm aware) for such a small matter like this. You are the admin on this community - you make the 'rules' if you like. I personally see no problem with this user leaving a link to their current profile from their anon profile (especially if they've made a high number of edits).
Really, it's up to you. If you have a problem with the page, you can delete it - it's always good to have an explanation but you wouldn't necessarily need one (though if you don't, that new user might leave the wiki if they ask you for it and you don't reply).
If you really want an explanation to delete it, make a policy on your wiki. It would look pretty stupid: 'this wiki allows no anon user pages' without a reason is a ridiculous rule, but that can be a reason to delete the page :P.
Let's put it like this: imagine that you forgot your password to your current account and so created a new one and everyone on the wiki knew this new account was your old one. But, for newer users on the wiki, you want to make sure that they know the two accounts are linked. So, you add an 'aka new username' to your old profile (which has over 21 000 good edits like you do on the wiki you're talking about). However, an admin comes along and deletes your old profile and newer users have an idea that that old account is actually you. They don't know that those 21 000+ edits were made by you. And the reason: I dunno, I'll just make a policy is what you get from the admin. You now get no appreciation for those 1500 edits at all. :P
It's similar with that anon, they want to show others that they are the one who has made those edits - so why not let them do that?
I highly doubt that anyone in the future who is using that IP adress will make an edit on your wiki so there's really no problem with keeping it. :)