jl: first, don’t write “according to this psak”. It is not a psak and the whole thing may very well be false. Second- the tannaim, the amoraim, the neviim even, did not not have “biblical names”(unless novih is biblical in your view). The best I can say about this is what some posters suggested. Maybe the person had special problems- health, parnossoh or zivugim- and hence ,Rav kanievsky said that shirah is not an original name. This is about as far as I can take this whole discussion. In actuality, most names are made up and are fine.
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