Hi and welcome to Just Answer!"fully vested" - means ownership is not restricted - and as the owner you may sell the asset, gift it, use as a collateral, etc - without any limitations.I am not clear what do you mean under "through assignment" - but if the ownership is change - there might be a legal procedure to do that. For instance - if the stock is in your brokerage account and you want to transfer it to another person - that person might need to have a brokerage account as well.
Let me know if you need any help.
"without taking ownership" - means - you do not own assets - if you do not own asset - you may not gift it.
Because taking an ownership also means taking certain tax liability - seems as "by assignment" you want to re-assign your tax liability to another person - that will not work.
If you "instruct the company's counsel to put the vested shares into my daughter's name" - that will be treated as your constructive receipt of income with corresponding tax liability - even if shares were never credited to your account.
Sorry if you expected a different answer.
Yes - you may do that - but still you will be considered as constructively received these shares - even you never take possession of the shares.
That in particular means - if the total gift value is above $13,000 - you would be required to file a gift tax return.