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Joanna Borucka's body was found at the Pay and Sleep hostel in Southall on Friday 18 December.
It is believed the 41-year-old - who was originally from Poland - was last seen alive on Friday 13 November.
Investigations have led the Met Police to 50-year-old Petras Zalynas, who they 'urgently need to speak to in relation to Joanna's death'.
It is thought that the Lithuanian may have fled the UK for Europe, and he may now be in Germany.
An international manhunt is now under way.
Detective Chief Inspector Wayne Jolley said: "It is thankfully very rare for a body to be found in these shocking circumstances. I know it makes the news of Joanna's death all the more difficult for those who were close to her.
"Our investigation is progressing well. We have identified Petras Zalynas as a person who we need to speak to in order to find out what happened to Joanna. I'm confident there are people out there who may have seen Zalynas or who might know where he is. I would urge them to come forward.
"I would particularly appeal to London's Lithuanian community. If you know anything about the whereabouts of Petras Zalynas, please get in touch. You will be supported and your information could hold the key to unlocking this investigation."
An inquest into Borucka's death was opened on 5 January at West London Coroner's Court and adjourned until the Met's investigation has finished.
Tributes were paid to Borucka following the discovery of her body.
Hostel resident Martin told the Evening Standard: "She was my good friend. We had similar friends. Nice girl, very nice and friendly.
"A very good person."
Another resident by the name of Lisa said Borucka's boyfriend had gone missing.
She said: "She lived in the floor up at the top. We were told by one of the other Polish guys that she'd gone to Victoria coach station.
"No one could get hold of her but now we know why.
"Her boyfriend has gone missing, because she had someone living in the room with her. We don't know where he is.
"She was a lovely girl, she kept herself to herself."
Anyone with information is urged to call 101 or tweet @MetCC quoting CAD 4319/18DEC.
Alternatively, information can be provided to Crimestoppers, anonymously, by calling 0800 555 111.
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