You appear to be asking two very different questions.
First there is the issue of 'assign it where', as in what software or data are you working with? Is it a building layer that has no NAC attribute and you want to add? Is it a building layer that has two labels already and you want one? Are you creating it from scratch? Is it point labels on a map? What are you doing with this information? Without significantly more information we cannot make any software recommendations or answers.
It's possible there are geocoding locator services that can assign NAC addresses but I don't know, nor do I know what softwares they would be compatible with. A quick Google search on 'NAC locator' found this page. I also note an External Link at the bottom of the Wiki article leads to this page, which lists mapping services, software, and data for working with NAC.
Second, you appear to have an aribitrary rule problem in choosing an NAC address to use. The one with the majority of the building? Majority of the lot? Center of the building? That the building is accessed from? The front door? From the Wiki link now in your question:
An eight-character NAC specifies an area no larger than 25 metres by
50 metres, while a ten-character NAC cell is no larger than 0.8 metres
by 1.6 metres.
So if your building is larger than the smaller cell, perhaps you would want to use an 8 instead of 10 character address. This part of your question is the equivalent of 'how many decimal places in a lat/lon coordinate should I use?' The NAC system of using cell addresses means that sometimes a feature will fall in more than one cell (or not completely cover a cell), and you must decide the rules on how to resolve that.
This is fundamentally similar to the issue in a raster representation of data - if a feature falls only partially in a cell, how do you define the value for that cell? You have to make a rule. For example the feature is really important, so whatever it touches is going to be that value; alternatively if it covers half the cell count it as the feature, otherwise don't. Both approaches are valid, you just need to create a justifiable rule and apply it consistently.