Yes, it is completely legal to sign your name in a non-English language. The key legal fundamentals of a signature are consistency and the signer's intent, not whether the script is Latin or non-Latin.
The Easy Answer: Yes, You May Notarize Out-Of-State Documents.
The short answer is yes, notary publics are legally allowed to notarize documents from any state as long the notarial act is conducted within the geographical boundaries of the notary's state of commission.
There is no statute that addresses this question, but the general rule is that a Texas notary cannot perform a notarization on any document in which he or she is a party to the instrument or in which he or she has a personal or financially beneficial interest in the transaction.
The document must be notarized by the Consular Officer. A notarization therefore cannot be conducted by a German Honorary Consul or by a Notary Public.
The answer generally is “no” — Notary commissions are not transferable between states. If you are relocating to another state, you need to resign your current commission and apply for a Notary commission in your new state.
One of the most common mistakes that notaries make is not printing or signing their name exactly as it appears on their notary commission.
Though, notarizing a document in a foreign language which you cannot understand is not illegal, proceed with caution through the process to ensure you are completing your notarial duties completing.