Dropping unique constraint for column in H2

In the SQL language, identifier names can't be expressions. You need to run two statements:

select distinct constraint_name from information_schema.constraints 
where table_name='PUBLIC_PARTNER' and column_list='INFO'

and then get the identifier name, and run the statement

ALTER TABLE PUBLIC_PARTNER DROP CONSTRAINT <xxx>

You could use a user defined function to execute a dynamically created statement. First to create the execute alias (only once):

CREATE ALIAS IF NOT EXISTS EXECUTE AS $$ void executeSql(Connection conn, String sql) 
throws SQLException { conn.createStatement().executeUpdate(sql); } $$;

Then to call this method:

call execute('ALTER TABLE PUBLIC_PARTNER DROP CONSTRAINT ' || 
    (select distinct unique_index_name from in formation_schema.constraints 
    where table_name='PUBLIC_PARTNER' and column_list='INFO'));

... where execute is the user defined function that runs a statement.