Indian Passport and UK visa with different names

i am an indian national holding a tier-1 (PSW) visa. my indian passport is due to expire in few months time and i was planning to get a new passport from the high commission of india in London. i have a query with regards to the uk immigration, details of which are as follows

i got married last year and traveled to uk with my existing visa and passport (both have my maiden name on them). however now i plan to get my name in the passport changed to my married name (which involves change in my last name). once i have got the new passport, can i still travel on my OLD visa which will have my maiden name on it but will still be valid, in terms expiry date? would this pose any problem with UK immigration at the time of entering/leaving the UK?

would this pose a problem with indian immigration ?

i would be thankful if you can please answer this query for me

I don't think there will be any problem. Just keep ur old passport and marriage document with u when ever u travel.
At the time of visa extension in the application form just fill the section ' if u r known by any other name' and the new visa will be with new name.

I think you should fill out a change of circumstances form, highlighting your name change and how it is reflected on your passport. That way, if UKBA deem it necessary, they will re-issue you with a new BRP/visa. I don't think travelling with documents showing different names is a good idea.