Identity and fashion have a link in the physical world and thesis aims to claim the same to be true for the virtual world. If this is true then the same elements for businesses should apply to gain customers to buy and use product.
James Paul Gee: What Video Games Have to Teach Us About Learning and Literacy; and his article Affinity spaces: How young people live and learn on line and out of school, March 2018, Phi Delta Kappan 99(6):8-13
DOI:10.1177/0031721718762416
Jennifer Rowsell's research on digital literacies and identity
You might also check out Pop Culture Association's sigs for video games and fan studies.
Classic paper on avatar affect by Bailenson, the proteus effect Article The Proteus Effect Implications of Transformed Digital Self-...
I think avatar customisation for business is likely to have much more limited importance. If you look at the genres where avatar customisation is most complex and invested in by users it is generally long form RPG games. Players know they are engaging in 100+ hours of gameplay in deep involved storylines.