Buffers are now handled in the source project, not in the style project (in TileMill, one project controlled both data source and style; in MapBox Studio, they are now two different projects).
So, assuming you have access to the source file, click on the label layer, and under the configure tab increase Buffer Size to a number half the width of your widest label (or just estimate).
See the source quickstart, source manual, and styling labels doc.
If large labels are still an issue even with increased buffer size, it's possible to shrink text size for labels with high letter counts using regex expressions in the selectors. Something like
text-size: @text-size * 0.8;
text-size: @text-size * 0.6;
See this answer to another question on conditional labeling.