How can I insert a computed index field in Solr as a rendering variant, I tried creating a field variant with the same name but it didn't work.
There is no out-of-the-box variant definition item to fetch content from an index. But you can create it yourself.
One way would be to use NVelocity. A nice blog post on how to extend that can be found here: https://michaellwest.blogspot.com/2017/04/custom-rendering-variant-token-tool-for-sxa.html
Create your processor, add it to the getVelocityTemplateRenderers pipeline and use it in a template. The process method in the processor can get the item as parameter - with this information you can fetch the field from your index and return the value.
ps: you can make it more generic if you also pass the field name from the template to the processor
UPDATE: in SXA 1.9 a new pipeline was added called
processSearchItems that you can use if you are using the ootb Search functionality. The ootb processor in that pipeline will cast the item to a
SearchItem which includes an empty object. You could add a processor to that pipeline that fills that object with the needed data. The data from that object can be rendered with the Model variant (or Model iterator as from 1.9).