what happens if you are renting but split up

[AndThatsWhatIThinkOfYou]

and both names are on the agreement?

does one person move out and the other has to stay for the remaining time left on the agreement?

Or both give notice and move out.

I'm not sure what happens if you haven't finished the fixed term contracteg 6 or 12 months. After that it goes to a rolling contract and you can give 2 months notice. If you approach your landlord, they may waive the terms so you can go earlier.

it is a fixed contract for another 6 month's

Is there a break clause at all? You can try to agree with the landlord to let you surrender the tenancy earlier.

If both names are on, both will be jointly liable for the rent. I would try and negotiate with landlord; the minimum contract lengths are meant to protect tenants so if you are willingly leaving it might be OK.