Rank higher on Maps

Google says local ranking is relevance, distance and prominence. Everything that works maps onto one of those three.

Relevance: does your profile match the search?

Primary category is the single biggest lever. Secondary categories for everything else you really do.
Services and products filled in with real descriptions, not keyword lists.
Business description that says what you do and where, in plain words.

You can't change it, but a correct pin and a tight service area make sure you count for the right searches.
For multi-location businesses, one verified profile per staffed location.

Reviews: count, recency and replies. Steady beats bursts.
Your website's own authority: pages for each service and area, mentions from local news, suppliers, associations.
Consistent name, address and phone across directories.
Photos added regularly and posts answering common questions.

Does adding a city to my business name help?

It can, briefly, and then it gets the profile suspended. Don't.

Do Google Posts affect ranking?

Google says no directly; they do raise engagement, which counts toward prominence over time.