Here’s a case of someone asking me “you know OSM, can you explain this?” - and obviously I can’t in this case 
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Apparently, in some situations names of buildings (or a restaurant in this case) are not rendered on the default carto map, e.g. Way: Malga Frattasecca (95592028) | OpenStreetMap
As far as I can tell, this is correctly tagged and there are no other labels in the vicinity which would overlap?
I don’t see a tagging error. I think the name would probably overlapp with this picnic table so it is not rendered.
Unfortunatly I don’t see an easy way of fixing this. Lying to the database to get a “nicer” picture would be tagging for the renderer. So changes in carto would be requiered to display the name.
Yes, the problem ist the picnic table to the right side of the building centre. This happens regularly when different POI are very close together. What you could do is to map building and restaurant separately by removing the restaurant tags from the building and then place a node for the restaurant to the “upper” end of the building and give it the restaurant tags. This is in accordance with the general mapping rules and should solve the problem.
Carto is really performing as designed - the alternative renderers have similar issues if they also show the picnic tables.
Personally I think the mistake is mapping a cluster of individual picnic tables (which seem to move around anyway from a check on G**gle maps). It would be semantically cleaner, and easier to generate a nice map, to replace these by leisure=outdoor_seating.
Carto does have a concept of “low priority amenities” e.g. bench, which are rendered after text labels. You could propose that picnic tables are moved to low priority, but you’d need to have the evidence that this would improve the map in general, as opposed to fixing one example and creating new issues elsewhere, e.g. squashing an individual, very useful picnic table.
Sometimes in photos you can see picnic tables in front of the house wall. But there are only two picnic tables, not four. Other photos show four small tables with 2-3 chairs each, but these are not picnic tables! In winter pictures, you usually don’t see any tables in front of the house wall.
If you were there, correct it as you found it. The best way is probably to delete some or all of the picnic tables and use outdoor_seating as @phodgkin suggested.