Currently, it is possible to search the global rename log via Special:Log with a query such as this. That query (as of the 2018-05-02) returns a single result.
It is also currently possible to list the log events in the global rename log via the API, using a query such as this. However, it is not possible to filter the log by the old username via the API.
As an API user, I would like to be able to search the global rename log by old username using the API.