"Please put up an umbrella."
I accept that language is always changing, but I refuse to do so quietly.
To me, "put up" sounds like the opposite of "take down," "put away," or "discontinue." I might put up new curtains, put a car up for sale, put someone up to a dare, or put up with someone's behavior, and none of those are anything like "put away."
The only time I make that association is, say, if I store holiday decorations in the attic. At the end of the season I might put the decorations up in the attic. In this case it has everything to do with the relative location of my storage space and very little to do with the generic act of storing something. I could just have soon put them down in the basement or out in the garage.
Funny story! A few years ago I was completing some transaction that required the clerk to see my ID card. I set it down in front of her, she copied some information, said "Ok, put it up," and turned to find some forms. I didn't understand what she meant, and as I was thinking about it, she again said "I said you can put it up." Still not understanding, I quietly slid my card closer to her side of the table. Having found the form she needed, she turned to face me, saw my ID still out, and said "Please. Put. It. Up." She's staring right at me. People are waiting behind me and it's really getting awkward. Not knowing what else to do, I reach down, lift the top side of my ID off the table, and angle it towards her so she has a very comfortable view. She goes "PUT IT IN YOUR WALLET."
I get why she was losing patience with me, but I swear I had never before in my life heard that phrase used in that way, and I had no idea what was meant in that context.
It sounds like the opposite to be honest (as in "put up or shut up") but... I was going to say I agreed and that 'put up' fits more for a big garden umbrella or whatever, but honestly it sounds fine to me for a normal one too. 'Please open the umbrella' sounds weird because it's like you just want it open (bad luck indoors) instead of specifically raised
Ironically 'please open the umbrella' sounds better (to me) for the garden ones because they're on a fixed vertical pole anyway. Language eh? ;)