With the way it works now when someone likes a content you post (topic, post, file, image, etc), it shows up in your profile's activity, and you can also look up all the reputation a user has received in their profile.
For example, if you look at my profile right now, you'll see this item in it:
A list of reputations given and received is also available on this page: https://invisioncommunity.com/profile/145950-teraßyte/reputation/?type=forums_topic_post&change_section=1
If you follow a link from there, and the post is anonymous, you'll be able to figure out who made the post.
It doesn't work like this right now, it's a function that IPS would need to implement in the framework. I guess you can ask for this topic moved to the Feedback forum instead.
And no, it's not possible to create a custom modification to change this behavior, either. Because of the way reputation is currently implemented (traits), it's not possible to overload/extend the necessary code.