• BigQuery: identifier syntax, and @@variable for system variables.
• ClickHouse: N/A
• DB2: identifier syntax
• DB2i: identifier syntax
• DuckDB: identifier syntax
• Hive: ${hivevar:name}, ${hiveconf:name}, ${system:name} or ${name}. These are substitution variables (as in Oracle SQL terminology). They behave more like string-interpolation, that is, the values aren't automatically escaped by the system. A common example is to place the variable inside a string: SELECT * FROM users WHERE name = '${hivevar:USER_NAME}'. Also one can use the variable to parameterize table or column name (SELECT * FROM ${hivevar:my_table}). See also post in StackOverflow.
• MariaDB: @name (where the name consists of alphanumeric characters, ., _, and $), @'var name', @"var name", @`var name` (can be quoted as string or identifier). Also @@name for system variables.
• MySQL: Same as MariaDB. (System variables).
• N1QL: N/A
• PL/SQL: &name or &&name substitution variables (and :name bind variables - see parameters).
• PostgreSQL: identifier syntax (only in PL/pgSQL).
• Redshift: N/A
• SingleStoreDB:¹ @name (where the name consists of alphanumeric characters, _, and $), @`var name`. Also @@name for system variables.
• Snowflake:
  • $name (using identifier syntax for name)
  • $number references the column at this place (from left to right) in the table, see here
• Spark: ${name} Like with Hive, these are substitution variables.
• SQLite: N/A
• TiDB: Same as MariaDB and MySQL. System variables
• Transact-SQL: @name (using identifier syntax for name)
• Trino: N/A

Notes:

1. Tested SingleStoreDB syntax manually. Found no full documentation of variable syntax.