IOW, it was trivially easy to issue licenses without her name on them, something she could have done the first time the first gay couple walked in to her office.
No it isnt, it would be altering state documents. Kentucky state law is that the clerks name and a statement be on them no matter who in the office signs them, you arent getting it.
The judge while she was in jail, was having other clerks alter them, he ordered it, and could have done that to begin with instead of putting her in jail, and he only did that, when she threatened to sue over her name authorizing them when she didnt, learn how to read.