For example I have a query like:
const rows = await db.query(
"SELECT * FROM $1 WHERE email = $2 AND password = $3",
[tableName, email, password]
);
It gives me a syntax error.
This is not possible, parameterised queries only work for values (instead of literals) but not for identifiers. You will need to build the SQL string:
const rows = await db.query(
`SELECT * FROM ${db.escapeIdentifier(tableName)} WHERE email = $1 AND password = $2`,
[email, password]
);
(Assuming the db is a PgClient)
If you know the possible values of the tableName variable beforehand, you might get away without escaping; if you don't, you better also specify the schema explicitly.