In the US, a name, title, short phrase, or short expression, such as "Popeye," can't be copyrighted, as it is not considered an "original work of authorship." See US Copyright Circular 34.
Images, on the other hand, can be copyrighted, and it is a copyright in an image of Popeye that has entered the PD in the EU.
The mark "POPEYE," however, is still the subject of numerous trademark registrations in the US (and probably in the EU as well). Generally speaking, trademarks can persist for as long as they are used as source identifiers in commerce, so it is likely that the POPEYE trademarks will persist for as long as they have commercial value.
A quick search on TESS ("popeye[bi] and hearst[on] and live[ld]") shows 9 different US registrations for goods and services that range from comic strips to amusement park services to socks. The US trademark registrations mean that you can't sell Popeye branded goods or services that are similar to comic strips, amusement park services, socks, or other goods that Hearst brands with the POPEYE mark.
Copyrights and trademarks are separate beasts, but they can interact in odd ways. For example, if Popeye ever enters the public domain in the US (I say "if" because of the Mickey Mouse problem mentioned above by paiute), then you might be able to create new comic strips using the character and image of Popeye. However, Hearst's trademark registrations would bar you from using Popeye as a brand to sell your new comic strip.