The spelling with -y is an English influence (and in Spanish, this use of the Y only makes misspellings), but nicknames with -i are usual in femenine names:
Mari, Leti, Conchi,
Pauli...
Usually, they are made removing the ending in names which have an -i- (María >
Mari,
Patricia > Patri,
Leticia > Leti) or adding the diminutive suffix "-ita" (sometimes to a nickname Concepción >
Concha >
Conchita,
Dolores >
Lola >
Lolita) and then removing the ending "ta" (
Conchita > Conchi,
Lolita > Loli).
Lumia
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