Thank you all for your suggestions 💕

I think I won’t invest in a printer just for labels since the ink washes out.
I have used a laundry marker once for my son’s quilt, and I have ordered a special label from Etsy for my nephew’s quilt.
I have bought special fabric from spoon flower once.

Thank you!

I stopped putting quilting labels on my quilts. For the relatives passing them down through the family, I'm fine with it passing from word of mouth, or not. I decided not to put the labels on anymore to make the quilts truly reversible. When the label shows, it makes it look like the quilt is wrong side up, like a shirt on inside out.

If the quilt is for friends or strangers, they aren't going to know me anyhow when it moves on from the friend, and the stranger well, it's a stranger. They aren't family, they don't know me, so the name really means nothing.

To print on fabric you need to treat it first with a product called 'Bubble Jet Set' I think is the name. Then iron after printing has dried. I have done several of these and had no issues with washing out.
You can also buy A4 size fabric which has been treated, but is a bit more expensive.