As per wikipedia article, Arjuna was also called 'Partha' because he was son of Kunti (Pritha).
Why could not Yudhishtira/Bheema be called by this name?
In Sabhaparva of Mahabharta , after Pandavas leave for the forest for exile, this verse appears:
वनं गतेषु पार्थेषु निर्जितेषु दुरोदरे ।
धृतराष्ट्रं महाराजा तदा चिन्ता समाविशत् ।। [Sabhaparva 2-103]
Vanam gateshu partheshu nirjiteshu durodare |
Dhrtaraashtram mahaaraja tadaa chintaa samaavishat || [Sabhaparva 2-103]
The meaning of this verse is: 'O Maharaja, with the Parthas (to be understood as the Pandavas) being defeated at dice and being gone to the forest, anxiety encroached upon Dhritarashtra'
Thus, the term 'Partha' has been used in Mahabharata to represent "son of 'Pritha'/'Kunti'". Technically it may not fit for Nakula & Sahadeva, as they were biological sons of Madri. But since they were adopted by Kunti with equal love, they can also be referred as 'Partha'. However, it's mostly used for Arjuna.