My TOC looks perfect in Scrivener but changes in the compile. I want the chapter names to show and not the chapter numbers… 
Any ideas? See attached.
Document link conversion is handled by the settings in the Document Title Links compile format pane. Disable the Links use title prefixes only setting in that panel, and if you don’t want the chapter number itself, also disable the Update titles in document links with prefix and suffix settings option (the latter switches everything off, so if that’s all you want you can ignore the first option I mentioned).
It also looks like you are applying a Section Layout to your table of contents section that is not designed to accommodate its unique layout and use of tab stops to space the elements out on the page. Some compile formats come with a “Table of Contents” layout that will produce the best results. For the rest, one of the Layouts that indicates the main text formatting will be based on editor formatting.