'I haven't met Björk,' says Su Shaw, the Scottish singer and songwriter formerly known as Panda Su, 'but I have packed up some things to send to Björk. What's good about the label is, it's very much like a family, and of course she's part of that family. Yeah, I sent some speakers over to her, I helped wrap them up in some sleeping bags – I'm sure they were safely delivered! I haven't met her yet, but I'm hopeful of developing a friendship at some point.'

Shaw laughs as she says this, entirely unexpectant of the possibility of Björk asking her round for tea – and yet the possibility of it happening is exponentially closer than it has ever been, now that the pair are both signed to the One Little Indian label. Born in Wick in the north of Scotland and resident in Fife since the age of three, Shaw recorded for many years as Panda Su, and was an affiliate member of the Kingdom's fruitful music scene of the last couple of decades.

'Three years ago I was writing fan mail to King Creosote and chasing around KT Tunstall asking her to sign her name on a piece of paper which I would then take home and frame,' she told the Scotsman exactly a decade ago, noting that she went on to play with both artists at Anstruther's former Homegame festival that year. Nearly ten years of part-time musicianship followed – she also worked organising Scottish mountain treks for a charity based in St Andrews – until the decision was taken to go full-time with music, and reinvent herself as SHHE.

'I was never entirely comfortable or confident communicating how I wanted to sound, up until beginning the SHHE project,' says Shaw now. 'I decided I wanted to have a break from Panda Su for a while, because I had always intended to put out an album, but when I sat down to work on it, I wasn't really happy with anything I was coming out with. From that point I decided to make a conscious decision to just stop, and then to pick it up again when it felt right. In that interim period I learned how to create the music I really wanted to create, so now I'm much more in control of the recording and the production, and it felt so far away from my output as Panda Su that it just made sense to put it under a different name.'

The self-titled, recently-released debut album, which she will be playing songs from at her upcoming Celtic Connections gig, has a more sparse and contemporary electronic sound, as exemplified on the first single release 'Eyes Shut'; a song she released independently, until her friend Davie Miller – of the formerly One Little Indian-signed Finitribe – shared it on social media, and was contacted by the label the same day asking how to get in touch with Shaw.

That this all stemmed from a short period of musical self-reflection, however, kind of undersells the process; in 'becoming' SHHE, Shaw quit her job, sold her house and car, left her relationship and moved to Dundee – only a few miles, but also a whole world, away. 'I was living quite a solitary existence in the country, out by Tentsmuir,' she says. 'It was a beautiful location, but I always worked completely on my own, and I think that's been the difference for me. By no stretch is Dundee a huge city, but it was a big enough change for me.

'The only promise I made to myself was that I'd release music that was honest, and I wouldn't focus too much on what people thought about it. Eyes Shut was probably the first track that I'd written, produced and recorded myself, where I didn't even send it to anyone beforehand to ask for an opinion – I just wrote it, put it out and thought I'd see what happened. It was a strange lesson, because as soon as I did that, everything just strangely fell into place; and I wonder if that was always the thing that would allow that, just being honest and creating things in the way I wanted to. I mean, sometimes I think if One Little Indian hadn't come along, what would I be doing now? But it's not worth thinking about … '

The opportunity for creative collaboration in Dundee has inspired her; the tender dance performance in the video for 'Eyes Shut' was created with performers from Scottish Dance Theatre, while a mutual friend pointed out that Tommy Perman, formerly of FOUND, lives on the same street as Shaw overlooking the Tay. Yet much of the work she does isn't focused upon the city.

Even before One Little Indian came along – and ironically, given the Björk connection – Shaw was working on a collaborative project in Iceland (she enigmatically describes it as being 'about creating music using sleep and some of the landscapes out there') which may end up being an album or something else, while the songs she has created as SHHE so far have their roots in southern Europe; in terms of their subject, if not their sound. 'They explore themes of identity,' says Shaw, 'and I've been personally asking myself about that, so the album came from some of those questions.

'I was born in Scotland, so I'm Scottish, but I'm also half Portuguese, and I've never really explored that side of myself – I've been to Portugal, I have family there, but it wasn't until I went to Lisbon for six weeks over the summer to begin a project that I started exploring that identity and what it means, being based here but also feeling that … that Lisbon feels like home. I guess the question is, how much does your location or your environment influence your identity? Then when you move somewhere new, how much do you take with you and how much do you form there?'

Shaw speaks in terms of projects, and the sense is that what she does next may or may not be on record; she's keeping her options open. What she likes most about One Little Indian is that they're supportive of all of this, 'which is great for me, because I'm working on projects simultaneously and I don't always know what they're going to be, but everyone is quite open-minded about where they can go.' After this Celtic Connections show she wants to get out on tour around the UK and Europe, and to one city in particular. 'I still haven't played my official album launch in Dundee, so I'm looking to plan a date for that,' she says. 'I made the record here and was influenced very much by the city, so I'd really like to be able to play it here.'

The self-titled debut album by SHHE is out now on One Little Indian. She plays a Celtic Connections show at the Hug and Pint, Glasgow, Sat 25 Jan.