The standard Litvak custom (minhag) was, if one wanted to carry on with the same name, to call the subsequent child the same name as the first child, but as a secondĀ name, or second name in a hyphenated name. So, in my family's case, the grandfather Gdalya died in 1893. The next male offspring to be born was in 1896 and was called Gdalya, in memory of his father's now deceased father. Sadly, the child passed away withing a few months. My grandfather was born next, in 1897, and was called Elyahu Gdalya, remembering both his grandfather and deceased brother, but not in his case as a first name. The custom seems to have arisen out of a more general belief that naming children after relatives who died young invited the same fate.
Anthony Rabin
London, UK