The use of "give your 30 day" in your post sounds like US English to me. (This website is UK-based and many of our laws are vastly different to those in the US. So this probably isn't the best site to post questions about law on if you're on that side of the Atlantic).
Further, the standard notice period to end a periodic tenancy in the UK in 28 days, whereas it's 30 days in the USA. So that once again makes me suspect that you might be posting from the USA.
However, in
both countries the standard principles of contract law apply, meaning that you need to keep paying the full rent until your notice to end the tenancy expires, irrespective of whether or not you actually remain in the property until that time or not.
That's confirmed for tenants in the UK here
https://www.haart.co.uk/renting/tenant-advice/a-tenants-guide-to-ending-a-tenancy-agreement/
and for those in the USA here
https://homeguides.sfgate.com/give-30-day-notice-landlord-8278.html