Bishamon is both, the God of War and the God of Fortune.
Yato is not only given the title of the God of War and the God of Calamity, but is also a self-proclaimed Delivery God. Besides these:
• In Chapter 40, Fujisaki Kouto revealed that Yato is a "God of Depravity," meaning that Yato only knows how to steal and not to give, and that those people around him will suffer terribly.
• He has also decided to become a God of Fortune now.Source
Firstly, a God of Fortune is the title given to a God who brings good luck or uses his/her special abilities/powers to guard or enhance one's everyday life, and is, for the most part, not directly related to their powers (so as to say, they do not cast a spell which causes good fortune to come to someone).
Neither is one "born" a God of Fortune, or if one is, he/she may be stripped of the title should they bring dishonor to their kind (Similarly, other Gods can also be given the title of the God of Fortune.
As mentioned on the Wikia:
The Seven Gods of Fortune (七福神 Shichi Fukujin), commonly referred to in English as the Seven Lucky Gods, are the seven gods of good fortune in Japanese mythology and folklore.
They are some of the most widely worshipped, prayed to and wished upon Japanese gods in modern times, with figurines or masks of them being especially commonplace in small businesses.
Like for Kofuku, it's almost impossible (if not completely impossible) for her to become a "God of Fortune", given that she is the Goddess of Poverty.
As the Goddess of Poverty, Kofuku has always been hated and scorned. She was never allowed to own her own Shinki, possibly since it would augment her powers of disaster and create further destruction and chaos.Source
Secondly, a God doesn't have any "occupation". They are given the title based on their powers and how they use it. For example, Yato is technically only a God of War. The other titles were given to him based on how he used them. In the past, he used to be merciless and cruel, using his powers to kill other Gods in the battle, giving him the title of "God of Calamity".
Similarly, there is no reason why a God cannot be given two or more titles. This trait can be seen in real-life Gods and Goddesses as well. For instance:
Saraswati (Sanskrit: सरस्वती, Sarasvatī) is the Hindu goddess of knowledge, music, arts, wisdom and learning. Source
Parvati (IAST: Pārvatī) is the Hindu goddess of fertility, love and devotion; as well as of divine strength and power. Source
These are just two among many Gods and Goddesses who are believed to have more than one power for themselves.
I do not know much about Buddhism, however since the Gods of Fortune are based on real-life counterparts, of which you can read in detail here, it is not at all far-fetched for the Gods to wield more than one power or for more than two, or even ten Gods to share the same title. Even if their Buddhist counterparts in real life wield only one power or even none, the concept of the
Gods having more than one title is nothing new.