Is a name sticker with my name enough to prove a bike is mine if it gets stolen?
It may be better than nothing, but no.  There are free registries online that you can use to register your bike's serial number.  The shop where I purchased mine set me up as a part of the purchase.

Some home/renter's insurance policies require you to have pictures of the bike along with the registration. Pictures with a datestamp could help prove how long you have had the bike.