You could make a terms facet on your ‘full_name’ field. But in order to do that properly you need to make sure you’re not tokenizing it while indexing, otherwise every entry in the facet will be a different term that is part of the field content. You most likely need to configure it as ‘not_analyzed’ in your mapping. If you are also searching on it and you still want to tokenize it you can just index it in two different ways using multi field.
You also need to take into account that depending on the number of unique terms that are part of the full_name field, this operation can be expensive and require quite some memory.