Search in Lightning Experience

Here a few items to note related to search in Lightning Experience:

1. Not all standard objects and standard fields are searchable in Salesforce, check out this article, and this article to make additional fields searchable.
2. For custom objects, Allow Search option must be enabled.
3. You can filter your search result to a specific object.
4. Limit the number of results by entering more specific search terms. For example, enter the full name and company (Mike Jones Salesforce). 
5. As you type, you will see suggested records:
• Recently accessed items
• Results that match Name field values
6. After a record is created or updated, it can take a few minutes for the new text to be indexed and become searchable. A record doesn’t show in the search results until it’s in the index. Wait a few minutes and search again.
7. The search engine only returns results you have permission to view.
8. Ensure the object has a tab created. Objects without a tab aren't returned in search results, Tab visibility for the affected User's assigned profile is set to 'Default On' or 'Default Off' and not Tab Hidden.
9. If your search contains punctuation, phone, email, or special characters and you’re not getting the right results, try your search with white spaces in place of the punctuation, check out this article.
10. Formula fields are not searchable.
11. The field that contains the keyword does not need must be in the page layout.

Reference:

• Searchable Fields by Object in Lightning Experience
• Make additional fields searchable
• Find Information with Search
• How Does Search Break Up Information?
• Objects displayed in search results inconsistent between Users