I see two possible solutions:
If you always query that key value for equality you can use an a B-Tree index on the expression (`tags -> 'name')
create index idx_name on ways ( (tags -> 'name') );
A quick test has shown that Postgres does use the index to find if a key value is present in the hstore column, but apparently not for finding the associated value.
So you could try to add a condition to test for that key value as well:
select id
from ways
where tags ? 'name'
and tags -> 'name' = 'Wiehbergpark';
If all rows contain that key, it might not help though.