TinkerPop doesn't support RegEx matching out of the box. Some implementations (Titan and DSE Graph) do have some extra predicates though.
However, it's easy to implement your own predicate:
gremlin> regexBiPredicate = new java.util.function.BiPredicate<String, String>() {
......1> boolean test(String value, String pattern) {
......2> return value ==~ pattern
......3> }
......4> }
==>groovysh_evaluate$1@43f9dd56
gremlin> regex = {
......1> new P(regexBiPredicate, it)
......2> }
==>groovysh_evaluate$_run_closure1@354e7004
gremlin> g = TinkerFactory.createModern().traversal()
==>graphtraversalsource[tinkergraph[vertices:6 edges:6], standard]
gremlin> g.V().has("name", regex(/mark.*/))
==>v[1]