Very nice Question. Actually, there is a very beautiful reason why Lord Shiva is called as Saamba Sadashiva. The word Saamba is a combination of two words - Sa + Amba. ‘Sa’ means ‘accompanied by’ or ‘along with’. ‘Amba’ means mother, or Jaganmaata who is Umadevi or Parvati devi. Sadaashiva means ‘The one who is always auspicious’. Sadashiva is the name of Lord Shiva.
So, Saamba Sadashiva means ‘The Lord Shiva who is ever auspicious and is always accompanied by Umadevi’. Actually, this is a very good name since Lord Shiva is always accompanied by Umadevi. We must worship both Umadevi and Lord Shiva together. Lord Shiva is known as the ‘controller of the mind’ and Umadevi is known as Vaagdevi or ‘the goddess of speech’. Goddess Saraswati is primarily Vaagdevi, but along with that Umadevi is also Vaagdevi + the devata for pure knowledge. Goddess Parvati does the upadesha to Indra and other devatas and hence is Guru to them.
Indra and other devatas get shastra training from Lord Shiva whereas they get shaastra paatha by Goddess Parvati. Hence, both ParvatiParameshwara are the guru to Indra and other devatas. Lord Shiva and Parvati devi gives us an important message via this name. As discussed above, Lord Shiva is the controller of mind, and Goddess Parvati is Vaagdevi. If our manas and tongue both are together, and are clean then we can achieve our goals in life with success. And this cleanliness of mind/manas and tongue both is possible by the anugraha or blessings of SriParvatiParameshwara.
सर्वमङ्गलदातारौ पार्वतीपरमेश्वरौ।
गणेशस्कन्दसंयुक्तौ वन्दे वाञ्छितसिद्धये॥
Lord Shiva and Parvati devi, both are the bestower of all kinds of auspiciousness in life accompanied by Ganesha and Skanda (Subramanya/Kartikeya).
Hope this helps!
Jay SriRam!
Har Har Mahadev!
ShriKrishnarpanamastu!