Right now the lamp has a harp holder, while you have what's called an uno shade, specifically a slip uno shade. "Uno" is a design where there are threads on the outside of the socket. The shade has a ring that can be threaded so it screws directly onto those, or it can be a "slip" style like yours, in which case an uno ring screws on after it to hold it in place.
Replacing the socket is probably going to be easier than modifying the shade, so to answer your question directly: you need an uno socket with ring, and a slotted screwdriver for disconnecting and reconnecting the lamp cord.
Here is an Amazon result for a socket that will work:
https://www.amazon.com/dp/B000V568EG
Here's a very fancy brass one that would also work:
You can search around and find these lots of places online, and if you are in the US I think Home Depot and Lowes may carry these in store too.
It appears to be a generic USB rechargable lamp sold under many brands across the internet. It folds up flat and then the light can be telescoped out, and the base can be placed on a table or hang on a wall.
Here's one Amazon listing for this kind of lamp:
https://www.amazon.com/HTCAT-Stepless-Protection-Handicraft-Computer/dp/B0B75VJY92
I also saw it for sale on Aliexpress and Walmart's website.
The label inside reads 12V 20W max. The socket appears to be a bayonet socket of some kind (meaning you insert and turn slightly instead of screwing clockwise a bunch of times like a threaded bulb). Socket also has dual contacts in the bottom.
So maybe a 12V BA15D like this?
This is Colorpanda Gradient lamp.https://www.amazon.com/dp/B09XMLPYYQ/ref=promo_pdapsinfo?ie=UTF8&psc=1&m=A37QOAUONQRU0X
I'm pretty sure your lamp is an older model of this one available on Amazon https://www.amazon.com/Fangio-Lighting-W-1122-SB-Table/dp/B01HOXR4Q8
I don't know why this showed up in my Reddit feed or why I spent a half hour of my lunch break on this.
Garden lights look very nice both on and off. They fit very well into the garden design by the walkway. I also made it possible to enable them remotely, which is very convenient. Wrote a small review.
Macramé!!!
Mkono Macrame Lamp Shade Boho UNO Light Shade for Table Lamp of E26/E27 Light Socket Modern Handmade Woven Light Cover for Bedroom Living Room Office Decor https://www.amazon.com/dp/B08S3TW7T2/ref=cm_sw_r_cp_api_glt_fabc_GMJC633CSG4KCFPH7Q8R?_encoding=UTF8&psc=1
Looks like you could use a globe. Something like this:
​