Spouse name changed in Passport

#1
I hold an Indian passport and currently working in US on H1B. Am planning to get my Wife on H4 to US.

Question : My wife's name in my passport has her first name along with my lastname. However, in her passport my lastname is not mentioned.
Will that be a problem for immigration process?
Do I need get my wife's passport reissued with my lastname?
Any leads are appreciated.
 
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