What is better: Tag a building or name it. I want to set a Name and Category. What is to do, if in one building are two shops?
I am new here. 
Thanks for answers
Welcome Thomas,
the area should be tagged with building=yes. Even better building=retail in case there are only shops in the building.
Many people will tag the building with the shop tags when the whole building is 1 shop (e.g. a supermarket). If not, separate nodes are created within the building outline for each shop.
A shop is tagged with shop= and name=…
For the address, it also depends on whether the shops have different addresses or not. In case the address is for the whole building, put it on the building outline, otherwise on the node.
Please keep in mind that in some countries (e.g. Denmark), you should never put the address on the building, but always on a node.
In case you really want to add a lot of detail, you could start using the indoor tagging scheme to indicate the individual rooms in the building occupied by the different shops.
Names are tags! However, you should always have a main tag on a way, unless it is only used as part of a multipolygon, in which case it shouldn’t have a name. name is not a main tag.