You can look up ancestry in a program called Orchid Wiz. You can also look it up in the Royal Horticultural Society Orchid Registry,
The International Orchid Register / RHS Gardening
though you will need to go back manually generation by generation.
In this case the current correct name for your plant is Cattlianthe Secret Love. Cattlianthe is the name of a hybrid genus between species in natural genera Cattleya and Guarianthe. A cross between two species or hybrids is given a grex name instead of a species name. In this case it is Secret Love. Note the genus name is always capitalized. A species name currently is always in lower case. A grex name is always capitalized. Every seedling from this cross is called Cattlianthe Secret Love. All the seedlings will be slightly different one from another. 'Angel' is a clone name given to an individual from the cross. Clonal names are always capitalized and enclosed in single quotes.
The reason for the name change from Laeliocattleya to Cattlianthe is that one of the ancestors at the time the cross was made was considered a Laelia but is now a Cattleya, and another ancestor was considered a Cattleya but is now a Guarianthe. So all the ancestors are now considered either Cattleya or Guarianthe.