The simple answer to your question is No.
IP addresses are not linked to your name, address, personal details or even your inside leg measurement. ;;-)
Take care, though, that when paying at online shopping sites that the site is 'secure'.
You can confirm this because the address of a secure site will become click here, etc instead of just click here, etc.
Also, if Internet Explorer is your browser, you will also see a yellow locked padlock at the right-hand side of the bottom task bar.
If neither of these is the case - do NOT give out your credit/debit card details at that site.