I go to a drive-through pharmacy (because in the US, we have drive-through everything.)
The only "strange" encounter I had was a message on the phone about an hour after I dropped off an updated prescription. It went something like this:
"This call is for Mr. [my full birth name], this is [some lady's name] at [name of pharmacy]. I'm sorry but we're out of the... [ x ] milligram Estrogen? you were prescribed? We'll have it instock this Wednesday, we should have it ready for pick up around 3."
It made me smile just to hear the wave of confusion set in while she was speaking. I don't think she was against the idea of Mr. [my full birth name] taking estrogen, she just wasn't expecting it.
Normally my prescription just auto-refill, I get a text saying the next refill is ready, I stop through after work and there's almost zero interaction.