I don't believe there is anyway to apply boosting to an analyzer as you're suggesting.
One thing you can try, is to use the multi field type in your mapping. You could then apply your partial_name
analyzer to one version of the field, and your full_name
analyzer to the other version.
With this mapping, you could query both fields differently, but combined (perhaps in a bool query), and apply a boost to the query that is being conducted on the full_name
analyzed field.