You have mainly two options. One is to format the column you will paste in before doing the paste. The other is to make a change in the Text to Columns (T2C) function.
First, the formatting change. Unlike almost all the related questions, you are not starting with a file list and clicking to open an import file (CSV being the common format cited). So the usual "Too bad man, but Excel "helps" you here, whether you like it or not and whether it helps or not" does not apply. You have a spreadsheet open and can choose whether to bull ahead and be unhappy, or to format the column as TEXT, then do the paste. I want to think you're the latter group! If so, that's all it takes. You want it to be a text string once pasted and it will be. Done deal.
Second, the change in the working of T2C. You'll ask "Huh? Why? What's that got to do with anything?" Well, whether you hunt down and find the "legacy" `Import Wizard" and do your importing controlling its function (I know, YOU can't, but others might read this and it might apply to them), or just open a file, Excel uses the wizard so its setting matter. But guess what? When PASTING it uses those setting too!
So, if you used T2C directly, or indirectly by finding and using the "legacy" Import Wizard, and also used the "Delimited" path, making changes in it (picking or adding different delimiters), those changes affect future pasting into unformatted cells (as in "default format" exists, with no customization past that).
Consequently, I say for certainty that those settings in your session of Excel have included spaces as a delimiter. All you have to do to make the problem go away is to select a cell with something in it (T2C won't run if all that's selected is a blank cell), fire up T2C, choose the Delimiter path, and uncheck the box selecting spaces as one of your delimiters. Do NOT proceed further (unless you coincidentally wanted to do so for this cell!) but rather, click Cancel to exit immediately. The change will be preserved.
Now you can paste your data without Excel splitting it into columns using spaces as a delimiter.
Excel is like a dog with a bone. They created some aspect of this and then rolled it into the other two aspects. Probably, my bet, the Import Wizard, then thought, hey, write a way to enter it a little into the wizard and call the feature T2C, and then someone said "Hey, we can enter it even later when someone's pasting and let it "add functionality" to pasting!"
You know, as John Ringo might have written, "for certain values of add functionality"...
This has been addressed MANY times. There's even a post with an Answer by someone well-named here on Super User with a macro to do this changing for him. Then it seems he researched the internet and found a well-known fellow'd done the same long before. And let's face it, maybe dozens or hundreds or more others along the way:
Prevent Excel from converting text to columns
Second answer.
But really, AFTER remembering (always the hard bit, eh?), doing it by hand is a simple, easy thing to do. I have this come up all the time, not in manly data imports, but rather in emails of a kind from customers in which there's a lot of standardly formatted info and I want bits of it. I copy it and paste into a sheet in my "Useful Things" file and let the formulas collect the bits for me. Except I DO do other importing and occasionally end up doing this and it splits the cells/strings causing the formulas to go awry. A macro'd be nice then, to always just click before pasting on this sheet, but Ctrl-Z, then a couple mouse clicks and pasting again is so very easy that I've never bothered. But it might appeal to many.