Openstreet map version and business name

We use Openstreet map on our website to get the address of hotels.
On our map, the name of one hotel is an old name.
If i check on https://www.openstreetmap.org/ , i can see that the database is up to date and the name of the hotel is the good one.

I would like to explain my developper what he has to change to get the latest database.

I thought it would be just some URL calling so that we just need to update it but it seems to be more complicated.

I found this https://switch2osm.org/serving-tiles/updating-as-people-edit/ but as i am not a developper, i don’t understand it.
It seems we need to copy the database but it surprises me

Can anyone tell me how we can use an up to date database easily ?

First you should find out, where you get the map from. By what you describe, it does not sound as if you render the map yourself.

Can you show us a link to your site where the hotel name is wrong on a map?