Should my boyfriend and i be concerned about stds since monogamous?

No: If neither of you has an std to start with, and you're both truly monogamous, then you don't have to worry about stds.

Depends: If neither of you ever had a previous sexual partner you could toss this issue aside. However, there are STD's like HPV that are often asymptomatic in both genders but can reactivate & pass to a partner later. If you have both been screened & found to have no evidence of any past infections, monogamy would protect you both going forward.