I am a maharashtrian boy and buddhist by religion and my girlfriend is Hindu-brahmin. Actually we have same surname and no one from each others family share any relation. Can we marry each other ? Will our offspring be abnormal? Will it create any problem in the future?

If you don't share any relatives, then there should be no problem with offspring.

I don't know the laws of marriage with your religion but I don't THINK having the same sur name would be a problem because it would be totally unethical really..

I don't know what religious/cultural difficulties you may or may not have, but genetically your offspring will be no different than other babies.