The primary field is always the first column in any table, and cannot be deleted, moved, or hidden. The name is meant to be a short, unique representation of each record in your table.
The primary field is required so that it can be used as a brief description of a record in other parts of the UI. For example, if you link a record to another table, we show the value of the primary field in a small card representing the linked record:
We also use the primary field as the title of record cards, which we show in the iOS app and a number of other places:
The primary field is most often a text type field, but it can also support most other field types, including date, number, autonumber, and formula field types. However, the primary field will not support attachment, checkbox, single select, multiple select, rollup, lookup, and count fields, or links to other records.
If your table does not lend itself particularly well to a single unique primary field, a useful technique is to set the primary field as a formula type, and to compose the name of each record using values from the other fields in your table. To learn more about how to do this, you can read Using a Formula in the Primary Field.