IANAL, if the idea is the same, but the name is different, this is not usually enough to keep you out of trouble. Even if the look-and-feel is modernized.
The complicating factor is the fact that copyright and IP protections vary greatly country by country.
It is safer to try to get a license. However, for old titles, this may be difficult as there is no way to find representation unless it is too late. Companies have long since disappeared, been bought, etc. But, copyright can still be asserted by the originator or by the recipient of the assets of a company sale. And, look-and-feel gets grey pretty quick.
All in all, knocking off an old title with a few look-feel and game rule changes should be pretty safe, but licensing is the only way to be sure to not paint a target on your back should you actually start generating noticeable revenue. Look at Hasbro vs Scrabbulous for example.
PS: According to the book "High Score!", Sega published the original Snake, which means they likely control the rights to it, if they still do. So many variants exist that they likely have lost the right to assert copyright protection.