This is a known limitation. What you want to do instead is use their Search APIs for doing a full text search.
You can write a entity modification listener that updates the search index every time the entity is modified. This listener can then queue a job (via task queues) that will update the search index.
Now in the screen where you are displaying the search box, you can use the Search APIs to fetch the result.
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Or, the alternative is to live with a prefix only search query.