Would you ask to change the job title before or after getting hired knowingly it is a data scientist role?

Would you ask to change the job title before or after getting hired knowingly it is a data scientist role? For example , certain companies would labeled this role as an analyst or research analyst, but the job description and responsibilities are 90% of a data scientist. Would you ask for a title change to reflect what is current in the market? If so, at what stage would you ask? Reason being, if you were to leave for a data scientist role elsewhere, your new company might not view your analyst role an actual data scientist, thus potentially rejecting your application.

I'm assuming companies wouldn't want to pay top dollar for an actual data scientist title and would love to keep you knowing you would have problems job searching. That's just my hunch.

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