Does it matter? If its an own brand they won't be advertised regularly, perhaps occasionally as part of a special offer.
Its not like Always or Tampax or Bodyform, all brands in their own right so you see the adverts and everyone is aware of them. I buy supermarket own brand sanitary towels, have done for years, and I couldn't even hazard a guess at what the range is called.
Libby is a lovely name, I think you'd be daft to change her nickname now, especially if she is used to it.
I think you are over reacting a bit tbh. I googled "libbi" and it didn't come up (the tesco product) in the first few pages. They will no doubt rebrand/rename again in a few years. Sainsburys own brand sanpro used to be liberty. No idea at all why I remember that!
I couldnt call my dd flora ,because dh couldn't get past the margerine connection. tit. You will always find some prat singering whatever you casll your child unless its hannah,sophie,olivia,jessica et al. Elizabeth and Libby ar lovely