Pronounced a store, it is the Irish vocative case, as in a form of address, so, the 'a' translates as 'Oh' and 'stor' means treasure, as in a 'store of goods', 'treasure stored up', it is a somewhat shortened form of 'a stor mo chroi' which means, literally 'oh treasure of my heart', so it means 'o treasure', which one could replace with ' oh darling', 'dear' and the like but it does not MEAN 'oh darling' it MEANS 'oh treasure' ('my' implied) and it certainly does not mean and will never mean 'forever' which is of course 'go bragh' as in 'Erin go Bragh'; you might be familiar with the form for writing letters 'a chara' which literally means 'Oh dear', we shorten it to 'Dear'; English does not have a vocative case as our language is not inflected, but we use words in a vocative sense, like 'Hey you' or when we address someone before we say something else, like 'Joe,.....';

so in that song quoted above the last line is 'Come and take my name Oh treasure' (of my Heart) or by implication, 'my darling or some other endearment, but literaly it means 'oh treasure', & definitely does not mean 'forever'; the vocative causes the consonant change of lenition (softening, called seivú in Irish) in the word that follows, but 'st' is a consonant that does not change, eg to say oh Mary it would be 'a Mhuire' pronounced (in some parts of Ireland) 'uh whyra' not 'uh myra';