When viewing myheritage.com on a Macintosh using Safari names appear as "Unknown" - even when it says "This is you - Unknown" (myheritage-2.jpg)! However, the "Invite close family" section lists correct names (myheritage-3.jpg), even though those same people's names are shown as "Unknown" elsewhere (myheritage-4).
You see unknowns in your family's tree, not because of your browser, but because of language issues related to building a family tree in more than one language in our Family Tree Builder software.
Your family's tree is built with the software and is set to display both English and Swedish names in the tree. The issue here is that it's not enough simply to add a second display language in the program - one must also translate the names in order to display them in that language. If the names haven't been translated they will show up as "unknown" after publishing.
If you switch your family site's language to Swedish, you will see the names appear correctly, including your own.
Here is an FAQ item you can show to the Site Manager of your site to help him/her correct the problem: