Whose name goes on the checks for conservator?

ginab616, no, airfare is not reimburseable for anyone. Even the Executor would have to have the approval of probate court for any expense related to settling the estate.

Is air fare to the funeral for adult children reimbursable from the estate?

Discuss this with the bank. Generally the checks show the name of the account owner. You do not have to show your name at all, just be the signer on the bank records.

In our instance both my name as conservator and my moms name are listed on the checks.