Can a couple share the Quarantine residence in Norway provided by one person's employer?

Be aware that my answer describes the current situation. If you are not going to Norway until next year, it is very much possible, and I would even assume, that relevant details of the regulation have changed by then.

You are right that most persons entering Norway are currenty subject to a 10 days quarantine and the general rule is that the period must be spent in a designated quarantine hotel. There are three relatively clear-cut, but IMHO very unlogical exceptions from the requirement that the quarantine must be spent at a designated hotel. Note that these are not execptions from the quarantine requirement, just an exception from the rule where the quarantine must be spent:

1. Persons who are permanent residents of Norway. In public information and also in circulars to the border police, the Norwegian authorities have clarified that this exception also applies to people moving to Norway to take up residency as long as they have registered as residents in Norway before travelling there. It is recommended to quarantine at a place for yourself, but it is not prohibited for these persons to stay at their own home together with members of the same household, who have not been abroad.

2. Persons who are residents abroad, but own residential property in Norway. These persons are allowed to stay at their own place as long as it is a permanent location (a house, flat, hut or cabin and not just e.g. a caravan or a boat) and provdes all necessary facilities, so that you don't have to share e.g. kitchen, toilets or bathrooms with other people. If a group is travelling together and one of the persons own a property, the entire group is allowed to quarantine together at that place. It is indeed required to own a place to stay. Renting a place is not sufficient.

3. Workers who are coming to Norway if the employer provides sufficient single occupancy lodging for the quarantine period.

You are hoping to take advantage of the third exception, but it clearly only applies to workers (not people travelling together with workers) and even if your wife had been employed by the same company, they would have to provide you with separate housing facilities to fulfil the single occupancy requirement.

Even if it is not especially mentioned, the third exception does however rather apply to short-term contract workers and not foreigners who are permanently employed in Norway, since they are also with few exceptions permanent residents and therefore covered by the wider and less restricted first exception. If you register your new residency before travelling, both you and your wife can make use of that exception and stay together almost whereever you like. It does not matter if you rent or buy your own place to stay or if you are provided a place to stay by your employer.

Followup to the additional questions:

To exception 1: It means that you have to register in the National Population Register before travelling to Norway. This option is mentioned in the public information from the government and also clarified in cirular G-26/2020 to the border police, which contains all the relevant details for the interpretation of the regulation.

The people who have not been abroad does not refer to your case. I was just trying to point out that if two persons live together in Norway and one of them travels abroad and come back, that person is allowed to use the common home during the quarantine period, even if it then lives together in that household with other persons, who have not been abroad.

To exception 3: I can't say much about your interpretation of this exception unless you reveal why you think that your marriage certificate is of any relevance. There is nothing, neither in the regulation itself, nor in information from the government or the health authorities indicating that persons travelling together with workers are covered by the exception. It is also clear that the employer must provide separate rooms for each employee covered by this exception. The English translations use terms like 'single room' and 'private room', but from the Norwegian text, it is clear and obvious that each person covered by this exception must be lodged in a separate room. So, there is nothing here stating that your wife is covered by this exception and even if she had been, it is blatantly clear that it is not possible for you two to stay together during the quarantine period.