To put it in a short way: No, it's not possible.
Your Mac only allows you to share a connection through a connection that isn't used yet. Your Wi-Fi adapter cannot connect to and create a network at the same time. For example, if you're connected via Wi-Fi, you can only share that connection to other devices using your Ethernet port, and vice-versa.
A possibility would be to buy a wireless access point (or wireless router) and connect its LAN port to your Mac's Ethernet port. Then you connect to the WiFi with the MacBook and share that connection through Ethernet to the wireless access point. You can then configure the access point to create a different network than the one you originally connected to.
Or buy a USB wireless adapter, which you use to connect to the existing Wi-Fi network. Then, share this network through your internal Wi-Fi adapter.
Alternatively it might be easier to just replace the current Wi-Fi router/access point you're connecting to with one that offers a guest network, i.e. one that doesn't require a password to connect to. These are dual-band routers, since they allow you to create two networks. Read more here: Run Your Home Network Like a Coffee Shop for Easier Guest Access and Family-Friendly Browsing