Return part of a string with variable length

I have data in a table column like below:

host=0.0.0.0 port=5432 dbname=database_name user=pglogicaluser
host=0.0.0.0 port=5432 dbname=database_name2 user=pglogicaluser

I want to write a query to get the database names only like below:

database_name
database_name2

I could come up with something like:

select substring(column_name, '.+dbname=(.*)$') from table_name;

However, I couldn't figure how to stop the extraction before the user keyword starts.