Hi @NinaH2407, unfortunately we wouldn't be able to accept a cheque in your maiden name, it would have to be in your current name in order for it to be applied to your account correctly. This is because the name written on the cheque has to match the name of the account holder for security purposes.
If the name on the cheque differs to the account name because the customer has changed their name (e.g. marriage) and the customer can provide documentary proof (a legal linking document such as a marriage certificate to prove the link between the names or in the case of divorce, a birth certificate to show the maiden name), it is normally acceptable for a financial institution to process the cheque.
You have two valid legal names, you're not obliged to change it just because you got married. You may also choose to change your name but keep the maiden name for professional purposes. For example, a doctor who got married may choose to keep her maiden name is it matches that on her medical degree on the wall in her surgery. So she does business in that name but may be known by a different name in her personal life.
This can all lead to checks with the "wrong" name on them, like you have received. But, if you can prove that the name on the cheque is indeed you, it should be accepted. If you recently got married, you likely still have ID in your maiden name. If Tesco refuses to accept it, use that ID to open a new account elsewhere in your maiden name and pay the cheque in there.
@NickJ is right, security checks need to be made, but it you can prove that you are the named person on the cheque there is no reason the cheque can't be accepted.