String[] alg = {
            "GOST3411WITHGOST3410",
            "GOST3411WITHGOST3410EL",
            "CRYPTOPROSIGNATURE",
            "GOST3411WITHGOST3410DHEL",
            "1.2.643.2.2.3",
            "GOST3410",
            "GOST3410DH"};

        for(int i = 0; i < alg.length; i++) {
            try {
                java.security.Signature sig = java.security.Signature.getInstance(alg[i], "JCP");
                sig.initVerify(cert);
                sig.update(data);
                log.info(alg[i] + ": " + sig.verify(signature));
            } catch(Exception e) {
                log.info("Error: alg[" + i + "]: " + alg[i] + "; msg: " + e.getMessage());
            }
        }

Error: alg[0]: GOST3411WITHGOST3410; msg: Ключ должен соответствовать алгоритму ГОСТ Р 34.10-94
GOST3411WITHGOST3410EL: false
CRYPTOPROSIGNATURE: false
GOST3411WITHGOST3410DHEL: false
1.2.643.2.2.3: false
Error: alg[5]: GOST3410; msg: no such algorithm: GOST3410 for provider JCP
Error: alg[6]: GOST3410DH; msg: no such algorithm: GOST3410DH for provider JCP

Privatekey:
ru.CryptoPro.JCP.Key.GostExchPrivateKey;
.toSting(): CryptoPro Gost Exchange PrivateKey with parameters:1.2.643.2.2.98
.getAlgorithm(): GOST3410DH

PublicKey: 
ru.CryptoPro.JCP.Key.GostPublicKey
.getFormat(): X.509
.getAlgorithm(): GOST3410