The site Behind the Name collects sourced and reliable information on the etymology of names. Note that the site has two parts, an "official" database endorsed by the site owner, and a "contributed" database created by volunteer editors. The volunteer editors also strive for quality, but the contributed names are in general less trustworthy than the official part of that site.
There are also some language specific high quality sites, e.g., Nederlandse Voornamenbank for names used in the Netherlands (mainly Dutch and Frisian names).
EDIT: Another interesting resource is Dictionary of Medieval Names from European Sources, as the name tells restricted to a certain time period and geographic region, but still with solid etymologies.