Does it matter whose name is first when filing a joint return?

No, it does not matter----but once you begin filing joint returns with a spouse, stay consistent every year.  Do not switch around and decide to have the other spouse first next time.  If you do that it will confuse the IRS and cause errors for you when you transfer the prior year tax file to the new one.

No. But it should be consistent each year.  If you want to change the order from last year Turbo Tax it may not work right and change all the places.