Help: Tier 2 dependent visa name variation

[mkptier2]

Name in marriage certificate is maiden name including father name as middle name. While in passport given name is first name only and last name is maiden surname without middle name. Example

Marriage certificate:
First middle last name

Passport:
First last name (father name is provided separately)
Spouse name added in passport

Let me know is that significant name difference that can cause dependent visa rejection?
Please suggest shall I proceed for visa application using this document or shall I change the name to spouse surname in passport before applying visa?

[mkptier2]

please help admin