Rechargeable Li-ion battery pack
A voltage regulator on its own won't do.
In short, you need a proper Li-ion charger with load-sharing, preferably with some form of MPPT to get the most out of your solar panel.
It is also advisable to add a BMS to your battery pack, if it doesn't already have one, if only to make sure the batteries don't discharge too far.
ICs and modules exist that can do all or most of that. We don't do product recommendations here, but with the search terms above you should be able to find integrated solutions.
Li-ion batteries need to be charged with a specific algorithm (constant current first, then constant voltage, until the current has dropped below a certain value). A voltage regulator can't do all that.
You need load-sharing because the charging algorithm won't work properly when a load is connected directly to the battery.
You may need a form of MPPT because the solar panel won't deliver its full power otherwise, if it is not well-matched to the battery.