I also like this idea, the only issue I can think of is when multiple items of different repair needs will be placed at once. The idea of a 'multiple crafts needed' icon would pretty much work the same way as the repair icon we have now, because they won't know what is needed until they open the person's bazaar.

Having multiple icons on your name unless shrunken down will likely get lost especially in large groups, too small and it would be indistinguishable. It would be at most 5 icons for whatevers going on in the bazaar, then a possible linkshell crest if you are currently in one, and then a name, which may or may not be incredibly long depending on the character.

Perhaps a means to list the crafts needed through the menu. You normally click on the player to target them, then open up the menu to browse their bazaar, what if when you clicked on their name somewhere, it would list which professions were needed for repairs if they were up in the bazaar? IE: CRP/BSM/ALC etc.