When you tag someone in a post or photo on Facebook, that post also appears on that person's profile page. What is the equivalent for the #indieweb?
If someone sends a webmention to my home page, that is a way of tagging me in things. I may want to share this mention in my main home page feed (analogous to allowing peoples' Facebook posts to be shown on your Facebook timeline). In that case it's similar to a http://indiewebcamp.com/repost of the external content.
I would imagine this would look like a native post on my site but where the author is not me. Since I am not including third-person language anywhere on my site, I would just show the post without Twitter's "retweeted by ___" text. I may include an corner icon indicating it's a repost like how Twitter used to do it.
Facebook will by default allow friends' posts that tag you to show up on your timeline, and they give a way to hide the post from your timeline after the fact. I imagine people have strong feelings on whether they want this to happen automatically. Probably for the initial version I would make this require moderation, so if someone tagged me I would get a notification and an option to share on my home page.