Probably the best place to start is saints.sqpn.com. The guy who runs this site has put together all sorts of good lists, covering pretty much the whole standard Roman Martyrology, old and new, as well as many saints of the Eastern rites.
The Catholic Encyclopedia and Wikipedia are also decent places to search, as are many parish and diocesan saint pages. You will usually find these by means of a search engine. If you use Wikipedia, make sure to check different languages’ version of the page, as there’s a lot of difference in how much material is provided. Make sure to search links to saints’ famous churches, shrines, monasteries, etc. Look for primary sources, if you can. A surprising amount of material is available online now, and of course you can also check libraries for books!
Sometimes older sources will list someone as a Servant of God, Venerable, Blessed, or ordinary person, when newer sources show that their cause has moved along to another step of recognition.
Now, there are also a lot of saints who are genuine, recognized-by-bishops, saints from before the current canonization rules. (Blesseds, too.) You will be more likely to find these in older local martyrologies, or in compilation books of saints. Google Books and archive.org are good places to look for old saint compilations. This can also help you to find the saints’ days of Biblical patriarchs, etc.
There are also plenty of saints which have tons of documentation, but are just left to local martyrology calendars instead of having an official day in the Roman Martyrology calendar. This is no slur on the saint; heck, St. Patrick was only a local saint until the 1600’s. He just didn’t live close to Italy and England’s churchmen weren’t lobbying for Irish saints, that’s all.
Many saints have several days. Some of these are meant to commemmorate important days in the saint’s life, or transfers of relics to different churches, or special pilgrimage days to shrines. Others are caused by calendar adjustments (Julian to Gregorian, Trent to Vatican II, etc.) or attempts to avoid major holidays in order to promote celebration of the saint’s day. Generally multiple days will be celebrated only locally. Sometimes one diocese will use the date most important to them, while others choose a different important day. This is totally normal.
You will also have to look for spelling variants. This gets most challenging when you’re talking about phonetic transliteration spellings in, say, Latin or Portuguese, when the original name was in Chinese or Japanese or some other non-European tongue. Baby name books will often help with spelling variants, but sometimes can’t be trusted. This is also a consideration when looking up the saints’ days of Biblical patriarchs and matriarchs. They are often listed under their Latin Vulgate or Greek Septuagint spellings, or the spellings used in local languages, instead of Modern Hebrew or modern Bible spellings. (For example, Isaias or Ysaye for “Isaiah.”)
It helps to know what different languages use as their word or abbreviation for “saint.” For example, female French saints use the abbreviation “Ste.” German saints are “Heilige”, abbreviated as “H.” Spanish saints are “santo” for males, with the no-abbreviation-needed title “San”; and “santa” for females, with the abbreviation “Sta.” The Latin abbreviations are “S.” for one saint and “Ss.” for multiple saints.
The names of Christian feasts and holidays, important shrines, titles of God, and theological concepts are usually considered to be suitable Christian birth or Baptismal names. Often a name is associated with the day the child was born or the names of the godparents, as well as all the other reasons to choose names.
One particularly good compilation book for obscure female saints are Agnes Baillie Cunninghame Dunbar’s two volume book, A Dictionary of Saintly Women. Here’s Volume One, A-L, and Volume Two, M-Z.
Another is the old Latin book Sacrum Gynacaeum by Arthur Du Monstier. (The indexes are in the back, so I’ve linked to the back too. Check both indexes. If you get to the Topographical Index, you’ve gone too far.) It’s in calendar order, hence the need for the indexes.