How do I search Firestore by part of a name? like SQL LIKE

Firestore has no substring or full-text search, by design. Options, from simple to proper:

1. Keywords array. On write, store keywords: ["dark","chocolate","bar","choc","choco",...] (words plus their prefixes, lowercased) and query where("keywords", "array-contains", term). Works fine for short product names.
2. Search extension. Firebase has official extensions that sync a collection to Algolia, Typesense or Elastic. Real search, typos, ranking. Costs money beyond free tiers.

For 3000 products I'd do 1.

Honestly at 3000 small docs, loading them once and filtering on the client is not wrong. It's ~3000 reads per full load though, so cache it (persistent cache or just localStorage with a timestamp) instead of refetching per keystroke. That's the part that gets expensive. If the catalogue will grow to 50k, go with the keywords array or an extension.

Different angle, only if search is central to the product: this is where Postgres shines. pg_trgm with a GIN index gives you fast ilike '%choc%' and fuzzy matching out of the box. Not a reason to migrate on its own, but worth knowing when you pick a database for the next project.