The answer differs a bit between UK and American English.
In American English, the past participle of 'got' is 'gotten', so when you say "'I have got' would mean 'I have received'", that's not quite the case in America. You would need to say 'I have gotten' to mean 'I have received'. Instead, in American English, 'have got' is an idiom that is nearly identical in meaning to 'have'. In fact, interestingly, it matches 'have' in both the sense of 'to possess' and 'to be obligated to'. So 'I have to run' and 'I've got to run' also mean the same thing.
In the UK, as I understand it, 'got' is the past particle form of 'got', so 'I have got' does indeed mean 'I have received', which is not quite the same thing as saying 'I have'