if you are hoping for insurance to cover, you may have a few barriers
you may need to say you've been trying for at least a year and without a partner that may mean IUI's at a doctors office
I don't think you can show up and get DE covered w/o showing reason why DE is necessary, i.e. failed iVF's or premature ovarian failure.
if you have a friend you can bring with you and be "a couple" that would work best. Nicer to have someone you know. even better if it's a relative of yours so your genetics are part of the child. bonus would be same last name which makes you look married. MAKE SURE THAT PERSON IS COMMITTED TO PROCESS.
if you are young there are fewer insurance barriers such as age related infertility that prevent insurance from covering
not sure what you are trying to do but I wouldn't tell hospital your marital status. I'd say single. there are single women who have ex's insurance through a divorce decree. go with that. you can be single w/ a partner or w/o and using donor sperm.
i wouldn't tell husband either. I can't imagine he'd have to sign anything related to insurance. In example of ex providing insurance, he wouldn't have access to reason why your are receiving care. that would be confidential.