Naming after person who died after the birth of the child:

Some Poskim[1] rule that one should not name a child after a person who passed away only after the birth of the child. Other Poskim[2], however, rule that it is permitted to do so.

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[1] Divrei Yatziv Y.D. 162

[2] Teshuras Shaiy 1:5; Minchas Elazar 4:27