Jean Campbell, 53, was last spotted on CCTV at 10.30pm on Friday after leaving her flat in Bellrock Street near Cranhill Park in the east end of Glasgow.
Her body was found in the park by her husband John the next morning, while her German Shepherd dog was later found alive.
Police have stepped up patrols as inquiries continue into what they describe as a "particularly violent" attack.
MSP for Glasgow Provan Paul Martin said officers were working "around the clock".
He said: "I will continue to liaise with Glasgow City Council colleagues to consider what steps might be taken to make Cranhill Park a safer place at night."