Railway station names

Usually, just the city name is the main station. In the case of Basel, Basel SBB is the main station. All the other stations you are seeing are most probably bus or tram stops. General convention, a bus or tram stop is listed by the city name followed by a coma and another name like this: "CITY, bus stop".

(shouldnt i buy in advance a separate ticket from domodossola to milan or can i buy a last minute ticket in domodossola)?

When is this trip? Until early September, the Domodossola-Milan rail line has a closure between Stresa and Arona. There are rail replacement buses between Domodossola and Milan, but you need a reservation.

Dang, end of this august. Guess we will need to ride the bus.

Generally if there is only one major station in a place, it is named after the city. So Bern. Geneve. Luzern etc...
There are exceptions, but these are mostly due to history. Basel used to have a French, German and Swiss station, called Basel SNCF, Basel SBB, and Basel Bad resp. after the railways involved. Interlaken has Interlaken Ost and Interlaken West.

And then the SBB planner has all the local bus stops as well. And as many places will have a bus stop named "Bahnhof" or "Gare" or "Stazione" you will find lots of instances of "Bern, bahnhof". "Aigle, gare" etc...

But the SBB planner has a trick that allows you to ignore all that: You can just enter a street address....

Regarding Domodossola - Milano: That is going to be partly by bus. So maybe rearrange your trip so you end up leaving Switzerland for Milan via the Gotthard route in stead. But otherwise just book in advance on www.trenitalia.com, although you could also buy this ticket at the station. Even at the station in Mürren.

Yeah i dont want to change how i get to milan. Too many hotels to rearrange and will have already done the treno gottardo route earlier in trip. I would prefer different scenery. Ill just stick from domodossola on august 29th. Who knows maybe ill get lucky and they will be done with their repairs early (fat chance). So you dont think i will have any trouble buying a last minute ticket in domodossola from domodossola to milan?

Maybe i misunderstand but how can i put in a street address if i dont know which station i should be going into?

I reread what last poster wrote and it said i could even buy a ticket in Murren station. Ill be in murren for three nights, arriving aug. 26th in murren. No problem buying the ticket then from domodossola to milan?

I don't know why you would need to get a ticket from Domodossola to Milan. Why not get one from Mürren to Milano Centrale?

You don't even need to go into the station if you have a smartphone with the SBB app or a laptop with the ability to go to the SBB webpage.

You don't need to buy a different ticket for each bitty bit of the journey - just buy one for the origin to the destination. If you have any cards, like the half price card, you just apply them to the journey and the computer knows how to do the magic.

Tickets are not, generally, for trains, they are for a journey on a particular route, regardless of method of transport - regardless of boat, cable car, train, bus, etc. You don't need to split it all up.

I believe the OP has the STP, so in that case just adding a ticket Domodossola - Milano is the easiest option.

Trenitalia app