In most cases these are arbitrary numbers resulting from the isolation/gerneration of the cell line. E.g., imagine you seed single cells from an Hodkin Lymphoma patient into a 96 well plate and in well 60 you have a growing clone that you further cultivate, you name it HL-60....
Sometimes these number refers to the passages they have been through between source of origin to finally established cell lines. Also, it may refers to some experimental repeats of transfection to obtain a successful cell line. Hope it helps.
As Christian says, the origins of cell line names tend to be arbitrary, and most often a legacy from their original lab-note designation: HL (donor), 60 (the well number). The HL60 cell line was established in 1977 from a patient with acute myeloid leukaemia. . K562 was derived in 1971 from a 53-year-old female chronic myelogenous leukemia patient in blast crisis. .
Sometimes names are concatenated to indicate where/who developed them: MDA-MB-231 is from a pleural effusion of a 51-year-old caucasian female with a metastatic mammary adenocarcinoma: MDA – University of Texas M. D. Anderson Cancer Center; MB (metastatic breast); 231 (isolate number). .
Sometimes names come from the size of the species: e.g. p53 is the MW that corresponds to the electrophoretic migration of the protein under reducing conditions.
Sometimes there is little attempt to disguise their origins: HeLa, were derived from a malignant cervical tumour from a 31-year-old African American woman named Henrietta Lacks.
The only rationale naming conventions come from the catalogue numbers of repositories like ATCC, ECACC, DMSZ, Riken, DSHB, etc.