Display only table names with psql
In PostgreSQL (as described in documentation, The Information Schema):

SELECT table_name
FROM information_schema.tables
WHERE table_type='BASE TABLE'
AND table_schema='public';


For MySQL you would need table_schema='dbName' and for MSSQL remove that condition.

Notice that "only those tables and views are shown that the current user has access to". Also, if you have access to many databases and want to limit the result to a certain database, you can achieve that by adding condition AND table_catalog='yourDatabase' (in PostgreSQL).

If you'd also like to get rid of the header showing row names and footer showing row count, you could either start the psql with command line option -t (short for --tuples-only) or you can toggle the setting in psql's command line by \t (short for \pset tuples_only). This could be useful for example when piping output to another command with \g [ |command ].