Answering my own question:
My problem was that I didn't realise that my database name had some trailing whitespaces in the end.
TeraDriver uses single quotes to escape spaces and commas. This means that the database name should be in single quotes. If there are no single quotes, spaces and commas are considered to be the end of parameter value. If there are single quotes in database name, they should be presented as two single quote characters.
'Database-Name '
Whatever is within single quotes will be used with sql query: "database Database-Name". To escape '-' we need double quotes. So both single and double quotes in correct order should be used:
"jdbc:teradata://HostName/DATABASE='\"Database-Name\"'"