We left at Shantanu wanting to marry satyavati, and her father demanding that his grandson be named yuvaraja.
Now - what shantanu did not possess - he could not give. The post of yuvaraja had already been allotted to devavrata, and as he was perfectly fit and suitable, there was no reason to take it back from him . But Shantanu was enamoured towards Satyavati's attractions and he was not at peace. He was depressed and sad.
Meanwhile - Devavrata was a devoted son. He couldnt bear to see his father so dejected. So he tried and found out the cause of his father's greif. When he found the reason - he approached dasaraj with a marriage proposal for his dad - whereby Dasaraj repeated his demand. To this devevrata promised that he would not claim the kingdom and that satyavati's offspring would be the yuvaraja. But the fisherman still persisted. He said, while, you may not claim, your offspring may claim to be the rightful heir - then what will happen? To this - Devavrata took a terrible vow -"I will never marry and will remain celibate. Hence I wont have any sons - so there will be no challenges for satyavati's son, and I will see the image of my father in whoever is the present throned king in this descendency, and protect the kingdom to the best of my ability from attacks"
This was a "Bheeshma" decision - almost impossible for a normal man to fulfill - but Devavrata carried his oath as a dharma throughout his long (and in later stages very sad )life. Thus he came to be termed as bheeshma.