Thomas,
With the birth of a child to a married woman, there is a presumption of legitimacy, and the husband’s name will normally be entered automatically (and without him needing to be present). With an illegitimate child, the father’s name will only be entered if he was present at the registration and confirmed paternity. Otherwise that section is left blank. Plus you will note that the word “formerly” is deleted by the mother's name. Since she wasn’t married, there’s no maiden name, eg Benson or Baxter, to record. So the births were clearly recorded as illegitimate.
Now when it comes to the children marrying, they will be asked for their father’s name, and occupation. In some cases they may know that. In others, they may not. Some folk wished to avoid the embarrassment of being illegitimate and, if they didn’t know who their father was, they just made something up. (No documentary proof was required). That might have happened here. I assume you have looked for a William Gillanders death pre 1901, occupation blacksmith, but not found one? In that case, the likely inference is it’s not accurate. There was a William Gillanders, who died in Lisnaskea workhouse in 1895 aged 68. He was a labourer, not a blacksmith. He was married. The workhouse were fairly accurate about marital status because they needed to know about next of kin, in case the next of kin could support the person, or alternatively in case they too required support. So I suspect this is not Mary Jane’s partner.
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_retu…
One option is to look at the children’s baptism records. Family was Church of Ireland, according to the 1901 census. Lisnaskea Church of Ireland has baptisms from 1804 onwards. There’s a copy in PRONI in Belfast. You could look up all the children’s baptisms to see if a father is named. With illegitimate births it will sometimes say: “reputed father X” or similar. Or sometimes the father may even have been present.
You might also find Mary Jane’s own baptism in the records. This may be Mary’s death in 1906. If so, she was a spinster. So not married:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1906/05569/4563776.pdf
The admission records for Lisnaskea workhouse don’t appear to have survived which is a pity, as that would have been another possible source.
I noticed this death in Feb 1871 for William James Gillanders in Brobrohan. He was aged 3 months. Informant was Catherine Gillanders, also of Brobrohan. That’s presumably William James born November 1870.
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1871/020782/7290265.pdf
So who was Catherine Gillanders? A sister, or Mary Jane’s mother, or an aunt?Possible death here in 1908, again in the workhouse:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_retu…
Can’t find her in the 1901 census. There were only about 30 women in Lisnaskea workhouse in 1901 and she doesn’t appear to be amongst them.
There’s no Gillanders household in Brobrohan or Grogey in the Valuation revision records for 1864 – 1878 on the PRONI website. So either the family were lodging with someone there or their house was of too low a value to be recorded. Or perhaps they didn’t live there very long.
Possibly DNA testing may be a way of matching with others who have additional information about the family. (Though it;s wise to be careful with illegitimacy, as not everyone welcomes news of such ancestors). Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.
The North of Ireland Family History Society is running an Ulster DNA project in conjunction with FTDNA and can offer testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).