If a person pronounces a word with the sound /ɒ/, for example not, but says /kɑr/ instead of /kɑː/, does this mixture receive a name?
There are some regional English accents that naturally have /ɒ/ in 'not' and /ɑr/ in 'car' but I assume you are talking about someone that has an accent that combines features of more than one region, country, social stratum etc. - e.g. RP and General American.
I do not know of a specific linguistic term that refers to this, but the term colouring is sometimes used to refer to the influence of one accent on another, e.g. 'General American with some RP colouring' or 'regionally coloured RP'. Synthesis or synthetic might be an appropriate term to describe an accent that shares an equal number of features from different accents, but it does not, as far as I am aware, bear this specific linguistic meaning.