Yes, endnote has this facility. you right click in the formatted citation, and select “edit citation” at the bottom of the menu, and then choose “more…” from the bottom of the list. Add the text you want to appear followed by a space.
If you work in the unformatted (aka Temporary citation) it may be easier to add the text you want followed by a \
{e.g. \Author, year #3344}
which will be formated correctly, assuming you are using a numbered style that is normally expressed as [number] in square brackets.
If life if more complicated:
If you are using a style that usually superscripts the number, but want this one to appear in brackets because of the text doesn’t look right if followed by a superscripted number, then you might consider using hidden text to hide the citation itself, and type how you want it to appear. MInd you, do this as the last step before submitting. I hoped that you might be able to use the Author (year) option, but it puts the text out side square brackets if you format it as [Bibliography Number] ending up with e.g. [1] – but without the prefix, they would be easy to search for and you could type in the whole of the text and the number in new brackets and hide (hidden text font) the endnote inserted bracketed number. I prefer this to using endnote to list in bibliography only, as then you can’t find it later, but with hidden text you can see the number and note if they don’t correspond to your manually inserted version.